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1. InΔPQR, given that S is a point on PQ such that STIIQR and PS/SQ=3/5 If PR = 5.6 cm, then find PT.
2. InΔABC, AE is the external bisector of <A, meeting BC produced at E. If AB = 10 cm, AC = 6 cm and BC = 12 cm, then find CE.
3. P and Q are points on sides AB and AC respectively, ofΔABC. If AP = 3 cm,PB = 6 cm, AQ = 5 cm and QC = 10 cm, show that BC = 3 PQ.
4. The image of a tree on the film of a camera is of length 35 mm,the distancefrom the lens to the film is 42 mm andthe distancefrom the lens to the tree is 6 m. How tall is the portion of the tree being photographed?
5. D is the midpoint of the side BC ofΔABC. If P and Q are points on AB and on AC such that DP bisects <BDA and DQ bisects <ADC, then prove that PQ II BC.
6. If a straight line is drawn parallel to one side of a triangle intersecting the othertwo sides, then it divides thetwo sidesin the same ratio.
7. If a straight line divides anytwo sidesof a triangle in the same ratio, then the line must be parallel to the third side.
8. ABCD is a quadrilateral with AB =AD. If AE and AF are internal bisectors of <BAC and <DAC respectively, then prove that EF II BD. In aΔABC, D and E are points on AB and AC respectively such that AD/ DB = AEC/EC and <ADE = <DEA. Prove thatΔABC is isosceles.
9. In aΔABC, points D, E and F are taken on the sides AB, BC and CA respectively such that DE IIAC and FE II AB.
10. The internal bisector of <A ofΔABC meets BC at D and the external bisector of <A meets BC produced at E. Prove that BD/ BE = CD/CE
11. If a perpendicular is drawn from the vertex of a right angled triangle to its hypotenuse, then the triangles on each side of the perpendicular are similar to the whole triangle.
12. A man sees the top of a tower in a mirror which is at a distance of 87.6 m from the tower. The mirror is on the ground, facing upward. The man is 0.4 maway fromthe mirror, andthe distanceof his eye level from the ground is 1.5 m. How tall is the tower? (The foot of man, the mirror and the foot of the tower lie along a straight line).
13. In a rightΔABC, right angled at C, P and Q are points of the sides CA and CB respectively, which divide these sides in the ratio 2: 1. Prove that
(I) 9AQ2= 9AC2+4BC2 (II) 9 BP2= 9 BC2+ 4AC2(III) 9 (AQ2+BP2) = 13AB2
14. ABC is a triangle. PQ is the line segment intersecting AB in P and AC in Q such that PQ parallel to BC and dividesΔABC into two parts equal in area. Find BP: AB.
15. P and Q are the mid points on the sides CA and CB respectively of triangle ABC right angled at C. Prove that4(AQ2+BP2) = 5 AB2
16. In an equilateralΔABC, the side BC is trisected at D. Prove that 9AD2 = 7AB2
17. Prove that three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians ofthe triangle.
18. If ABC is an obtuse angled triangle, obtuse angled at B and if AD^CB Prove that
1.AC2=AB2+ BC2+2 BC x BD
19. Prove that in any triangle the sum of the squares of anytwo sidesis equal to twice the square of half of the third side together with twice the square of the median, which bisects the third side.
[To prove AB2+ AC2= 2AD2+ 2(1/2BC)2]
20. ABC is a right triangle right-angled at C and AC= √3 BC. Prove that <ABC=60o
In Triangle ABC ,Angle B=90 and BD perpendicular AC, if AC=9 cm and AD=3 cm then BD is equal to
1. 2√2 cm
3. 2√3 cm
Let ABC be triangle and D and E be two pobcints on side AB such that AD=BE. if DP||BC and EQ||AC, then prove PQ||AB
in triangle ABC,if AD is perpendicular to BCand AD*2=BD.DC,prove that angle BAC=90 degree
If root 3 sin theta - cos theta =0 and 0<theta<90
find the value of theta
Proof of the theorem: ratio of areas of two similar triangles is equal to the square of the ratio of their corresponding sides.
through the midpoint m of the side cd of a paralelogram abcd,the line bm is drawn intersecting ac in l and ad produced in e.prove that el=2bl
Prove that the ratio of areas of two similar triangles is equal to the square of their corresponding sides.
ABC is a right triangle, right angled at C. Let BC=a, CA=b, AB=c and let p be length of perpendicular from C on AB. Prove that
answer as quick as possible, tomorrow is my SA- 1 exam.
In the given figure ABCD is parallelogram in which DC=10cm and BC=4root3cm. AP is perpendicular to DC. If angle ADC = 60. Find:
(i) length of AP
(ii) Area of parallelogram ABCD
prove that in a right triangle the square of the hypotenuse is equal to the aum of the squares of the other two sides
In the given figure, AB||CQ and AC||PQ. If BP=1/3BC, find the ratio of the area of triangle ABC and triangle QCP
In a triangle ABC, D and E are points on sides AB and AC respectively , such that DE is parallel to BC.If AD = 2.4cm, AE= 3.2cm , DE = 2cm and BC = 5cm , find BD and CE.
In a trapezium ABCD, AB is parallel to DC and DC = 2AB E is point on BC such that BE : EC = 3:4. EF is drawn parallel to AB where F is a point on AD . Prove that 7EF = 10AB.
in the given figure angle A=90 degree,AD perpendicular BC.If BD=2cm and CD=8cm,find AD
triangle ABC is right angled triangle at B.side BC is trisected at points D and E.Prove that 8AE2=3AC2+5AD2
in a right triangle ABC , right angled at C; P and Q are points of the sides AC and BC respectively , which divides these sides in the ratio 2:1. prove that :
(a)9(AO)2=9(AC)2 + 4(BC)2
(b)9(BP)2 =9(BC)2 + 4(AC)2
(c)9[(AO)2 + (BP)2] = 13(AB)2
in an equilateral triangle ABC, D is a point on side BC such that BD = 1/3 BC. prove that 9 AD2 = 7 AB2
If O is any point inside a rectangle ABCD, then prove that OA2 + OC2 = OB2 + OD2
Prove that the sum of squares of a sides of a rhombus is equal to the sum of the squares of its diagonals......pls give answer.....u'll surely get a ''thumbs up''
In a triangle ABC, AB=AC. D is any point on BC. Show that AB2-AD2=BD.CD
1. Show that the area of a rhombus on hypotenuse of a right angled triangle, with one of the angles as 60 is equal to the sum of areas of rhombuses with one of their angles as 60 drawn on others sides.
2. BO and CO bisect angle B and angle C of triangle ABC. AO produced meets BC at P. Show:-
· AP bisects angle BAC.
side ab and ac and median ad of a triangle abc r respectively proportional to sides pq and pr and median pm of another triangle pqr prove that triangle abc similar to pqr explain step by step it plz
Two poles of height "a" m. and "b"m. are "p" m apart. Proove that the point of intersection of lines joining the tops of the poles to bottom of the opp. poles is given by :- h = (a * b) / (a+b) m
PLZ. ANSWER EVEN A WEEK PASSED BUT NO ANS. FROM MERITNATION
ABC & BDE R THE 2 EQUILATERAL TRIANGLES SUCH THAT D IS THE MID POINT OF BC .RATIO OF THE AREAS OF TRIANGLES ABC & BDE
in the figure of triangle ABC,d divides ca in the ratio of 4:3 .if DE// BC,then find the area of BCDE:are of triangle ABC.(diagram is not provided)
If BL and CM are medians of a triangle ABC right angled at A, then prove that 4( BL2 + CM2 ) = 5 BC2
In triangle ABC, DE is parallel to BC and AD:DB=5:4. diagonals DC and BE intersect at F. Find Area(triangle DEF) / Area(triangle CFB).
In triangle ABC, AD is a median . Prove that AB2 + AC2 = 2(AD2 + BD2)
In a quadrilateral ABCD, Angle B=90 degree, AD2=AB2+BC2+CD2.
Prove that Angle ACD=90 degree.
The sides of a right angled triangle are all integers.Two sides are primes that differ by 50.The smallest possible value of the third side is ............
prove that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides
If A be the area of a right triangle and b one of the sides containing the right angle, the length of the altitude on the hypotenuse is__________.
a) 2A/√(b2+2A2) b) 2Ab/√(b4+4A2) c)2Ab2/√(b3+4A2) d)2A2b/√(b4+3A2)
In triangle ABC if AD is the median then show that AB2 + AC2 = 2(AD2 + BD2)
Two similar triangles ABC and PBC are made on opposite sides of the
D is the midpoint of side BC of a triangle ABC.AD is bisected at a point E and BE produced cuts AC at the point X.Prove that - BE : EX = 3:1
in triangle ABC, DE ll BC. AD = 2cm, BD = 3cm, DE = 4cm. find BC. PLZ ANSWER FAST...NEED THE ANSWER URGENTLY....THUMBS UP FOR SURE....
In triangle ABC, angle A=60. Prove that BC2=AB2+AC2- AB.AC
E is an exterior point on diagonal AC of a parallelogram ABCD and DC produced meets BE at F. If side BC produced meets DE at G, prove that DB is parallel to GF
Prove that the area of
an equilateral triangle described on one side of a square is equal to
half the area of the equilateral triangle described on one of its
If the diagonals of a quadrilateral divide each other proportionally , prove that itAskis a trapezium
In an equilateral triangle PQR , if PT is perpendicular to QR then prove that 3PQ2 = 4PT2.
IN THE GIVEN FIGURE, DB IS PERPENDICULAR TO BC, DE IS PERPENDICULAR TO AB AND AC IS PERPENDICULAR TO BC. PROVE THAT BE/DE= AC/BC.
i am a meritnation paid user
in equilateral trangle d is a pnt on bc side bd=1third bc prove that 9ad2 =7ab2
if AD is perpendicular to BC and BD=1/3 CD.prove that 2AC2=2AB2 +BC2
A vertical pole which is 2.25 m long casts a 6.75 m long shadow on the ground. At the same time , a vertical tower casts a 90 m long shadow on the ground .Find the height of the tower.
what is the difference between - median , altitude , perpendicular bisector and perpendicular - in a triangle?
In triangle ABC , AD is perpendicular to BC. Prove that AD2= 3DC....tried the question many tyms...cn sum1 pls explain with the steps.
In a triangle ABC , AB =AC and D is a point on side AC , such that BC2=AC.CD . Prove that BD =BC . PLEASE HELP ME MERITNATION !!!
What are various aspects of pythagoras theorem?
ABCD is trapezium, and the diagonals intersect at O... AO = x +5 , OC= x +3 , DO = x-2 and BO = x-1.
Find x if AB is parallel to DC.......
In triangle ABC points P,Q and R lie on sides BC, CA and AB respectively. If PQ||AB and QR||BC then prove that RP||CA
In an equilateral triangle ABC,D is a point on side BC such that 4BD = BC. prove that 16AD2 = 13BC2
In the figure - PA,, QB and RC are perpendiculars to AC. prove that 1/x + 1/z = 1/y
In the following figure, ABD is a triangle right angled at A and AC ⊥ BD. Show that
(i) AB2 = BC × BD
(ii) AC2 = BC × DC
(iii) AD2 = BD × CD
how to do this using pythagoras theorem ?
D is a point on the side BC of triangle ABC such that angle BAC= angle ADC. Prove that CA2 = CB x CD
In triangle ABC, AB=AC and BD is perpendicular to AC. Prove that BC2=2AC.CD
In given figure, is a right triangle PQR, right angled at Q. X and Y are the points on PQ and QR such that PX : XQ=
In triangle ABC, P and Q are points on the sides AB and AC respectively such that PQ is parallel to BC. Prove that medium AD, drawn from A to BC, bisects PQ.
Please explain the exterior angle bisector theorem!!!
SAMPLE PAPER/MODEL TEST PAPER
SUBJECT – MATH 10TH CBSE SA 2 2011
Section – A
1. A number is selected from numbers 1 to 25. The probability that it is prime is:
(a) 5/6(b) 1/3(c) 1/6(d) 2/3
2. If the angle of elevation of the top of a tower from two points distance a and b from the base and in the same straight line with at are complementary, then the height of the tower is:
(a) a/b(b) ab(c) √ ab(d) √a/b
3. The perimeter of a triangle is 30 cm and the circumference of its in circle is 88 cm. Then area of triangle is:
(a) 420 cm2 (b) 140 cm2 (c) 70 cm2 (d) 210 cm2
4. If the first term of an A.P. is 2 and common difference is 4, then the sum of its 40 terms is:
(a) 2800(b) 16000(c) 3200(d) 200
5. The surface area of a sphere is same as the curved surface of right circular cylinder whose height and diameter are 12 cm each. The radius of the sphere is:
(a)12 cm(b) 4 cm(c) 3 cm(d) 6 cm
6. If the circumference and the area of a circle are numerically equal, then diameter of the circle is:
(a) π/2(b) 2π(c) 2(d) 4
7. AB and CD are two common tangents of circles which touch each other at C. If D lies on AB such that CD = 4 cm, then AB is equal to:
(a)12cm(b) 6 cm(c) 4 cm(d) 8cm
8. A tangent PQ at a point P of a circle of radius 5 cm meets a line through the centre O at a point Q such that OQ= 12 cm. Length PQ is:
(a) 13 cm (b) 8.5 cm(c) √119(d) 12 cm
9. If three coins are tossed simultaneously, then the probability of getting at least two heads, is:
(a) ¼(b) ½(c) 2/4 (d) 3/8
10. The area of in circle of an equilateral triangle is 154 cm2 .The perimeter of the triangle is:
(a) 72.7 cm(b) 72.3 cm(c) 71.5 cm(d)71.7 cm
Section – B
11. Prove that the tangents drawn at the ends of a diameter of a circle are paralled.
12.A bag contains 7 white, 4 red and 9 black balls. A ball is drawn at the random. What is the probability that ball drawn is not white?
13. Shoe that the points (7, 10), (-2, 5) and (3, -4) are the vertices of an isosceles right triangle.
14. Using the quadratic formula, solve the equation:
A2b2x2 – (4b4 – 3a4) x – 12a2b2 = 0
15. Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
16. Find the radius of circle whose area is equal to the sum of the areas of three circles whose radii are 3 cm, 4 cm and 12cm.
17. The line segment joining the points (3, -4) and (1, 2) is trisected at the points P and Q.
If the coordinates of P and Q are (p, -2) and (5/3, q) respectively, find the values of p and q.
18. Find the area of a circular ring whose external and internal diameters are 20 cm and 6 cm.
Section – C
19. If m times the mth tern of an A.P. is equal to n times its nth term, find (m + n)th term of A.P.?
20.Two tangents TP and TQ are drawn from an external point T to a circle with centre O. As shown in fig. or if they are inclined to each other at an angle of 1000 then what is the value of ∟POQ?
21. From the top of house, h meters high from the ground, the angle of elevation and depression of the top and bottom of a tower on the other side of the street are ѳ and φ, respectively. Prove that the height of the tower h (1+ tan ѳ cot ѳ).
22. A motor boat whose speed is 8cm/hour in still water goes 15 km down stream and comes back in a total time of 3 hours 40 minutes. Find the speed of the stream.
23. For what value of n are the nth terms of two A.P. is 63, 65, 67 ……… and 3, 10, 17……… equal?
24. Construct a triangle ABC in which AB = 6.5 cm, ∟B = 600 and BC = 5.5 cm. Also construct a triangle ABC similar to triangle ABC, whose each side is 3/2 times the corresponding side of the triangle ABC.
25. A bag contains 5 white balls, 7 red balls, 4 black balls and 2blue balls. One ball is drawn at random from the bag. What is the probability that the ball drawn is:
(a) Not white
(b) Red or black
(c) White or blue
(d) Neither white not black
26. PQRS is a square land of the side 28 m. Two semicircular grass covered portions are to be made on two of its opposite sides as shown in the figure. How much area will be left uncovered? [Take π = 22/7]
27. A solid composed of a cylinder with hemispherical ends. If the whole length of the solid is 104 cm and radius of each hemispherical end is 7cm, find the cost of polishing its surface at the rate of Rs.10 per dm2
28. If A (4,-8), B (3, 6) and C (5, -4) are the vertices of triangle ABC, D is the mid point of BC and P is a point on adjoined such that AP/PD = 2. Find the coordinate of P.
Section – D
29. Solve for x:
X4 +2x3 + 13x2 + 2x + 1 = 0.
30. The angles of depression of the top and bottom of an8 m tall building from the top of a multistoreyed building are 300 and 450 respectively. Find the height of the multi storeyed building and the distance between the two buildings.
31. Solve for x:
2 (x2+ 1/x2) – (x + 1/x) – 11 = 0
32. A class consists of a number of boys whose ages are in A.P., the common difference being 4 months. If they youngest boy is just eight years old and if sum of the ages is 168 years. Find the number of boys in the class.
33. Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are 7/5 of the corresponding sides of first triangle.
34. A car has to wipers which do not over lap each wiper has a blade of length 25 cm sweeping through an angle 1150 . Find the total area cleared at each sweep of the blades.
Two poles of height a and b metres are p metre apart . Prove that the height of each pole to the foot of opposite pole is given by ab/a+b metres.
ABC and DBC are two triangles on the same base BC.If AD intersects BC at O,show that ar(ABC)/ar(DBC)=AO/DO
Amar and Ashok are two friends standing at a corner of a rectangular garden. They wanted to drink water. Amar goes due north at a speed of 50 m/min and Ashok due west at a speed of 60 m/min. They travel for 5 minutes. Amar reaches the tap and drinks water. How far(minimum distance) is Ashok from the tap now?
IF THE AREAS OF TWO SIMILAR TRIANGLES ARE EQUAL,,PROVE THAT THEY ARE CONGRUENT...
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