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Syllabus

A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively (see given figure). Find the sides AB and AC.

explain this some in a little easy maNNER.PLS EXPERTSS

three mutually tangent spheres of radius 1 rest on a horizontal plane . a sphere of radius 2 rests on them.what is the distance from the plane to the top of the larger sphere?

a) 3 +√30 / 2 b) 3 +√69/2 c) 59/2 d)3+ 2√2

prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.

ABC is a right triangle right angled at B, such that BC = 6 cm and AB = 8 CM, find the radius of its in circle.

three circles of radius' s' are drawn in the first quadrant of the xy plane.the first circle is tangent to both axes,the second is tangent to the first circle and the x axis,and the third is tangent to the first circle and the y axis . a circle of radius rs is tangent to both axes and to the second and the third circle.

then the value of ( r / s) is

a)5 b)9 c)6 d) 10

PQ is a chord of length 8cm of a circle of radius 5cm. The tangent at P and Q intersect at a point T. Find the length TP?

CAN I GET THE CORRECT EXPLATION OF THIS EXAMPLE????

plz

^{}^{2}= AB * BNprove that the tangent drawn at the mid point of an arc of a circle is parallel to the chord joining the end points of the arc

240 students reside in a hostel.Out of which 50%go for yoga classes early in the morning, 25%have joined the gym club and 15% of them go for the morning walk.rest of the students have joined the laughing club.

A)what is the probability of students who have joined the laughing club?

B)what is the probability of students who have joined any class or club?

C)which value is depicted by students?

A circle touches the side Bc of a triangle ABC at a point P and touches AB and AC when produced at Q and R respectively. Show that

prove that the length of the tangents drawn from an external point to a circle are equal, hence show that the centre lies on the bisector of the angle between the two tangents?

At one end A of a diameter AB of a circle of radius 5 cm, tangent XAY is drawn to the

ab is a chord of length 16cm of a circle of radius 10 cm .the tangents at a and b intersect at point p.find the length of pa

Two tangents TP and TQ are drawn to a circle with center O from an external point T. Prove that angle PTQ = 2 OPQ.

P is the mid-point of an arc QPR of a circle.show the tangent at P is parallel to the chord QR

Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre of the circle.

Circle C(O,r) touches the circle C(o,r') internally at P. PB is a chord of larger circle, which intersects the smaller circle at A. Then prove that PA : PB = r : r'.

Ab is a diameter and AC is a chord of a circle such that angle BAC =30 .If then tangent at C intersects AB produced in D,prove that BC=BD

Two circles of radius r and r' touch externally at P. APB is a secant intersecting the circles respectively at A and B(other than P). Prove that PA/PB = r/r'

If an isosceles triangle ABC in which AB = AC = 6 cm is inscribed in a

If qb=5cm and pc=9cm then evaluate value of pa.

A chord of circle of radius 10 cm subtends a right angle at the centre.Find the area of the corresponding minor segment and hence find the area of the major sector?

Three circles are drawn with the vertices of a triangle as centres such that each circle touches the other two. If the sides of the triangle are 2 cm, 3 cm, and 4 cm, find the diameter of the smallest circle.

(a) 1 cm

(b) 3 cm

(c) 5 cm

(d) 4 cm.

Please give the working also..The radii of two concentric circles are 13 cm and 8 cm . AB is a diameter of the bigger circle BD is tangent to the smaller circle touching it at D.Find the length of AD

(A) (2+√5)/2

(B) 5/2

(C) √5

(D) √6

From a point P, two tangents PA and PB are drawn to a circle with centre O. If OP is equal to the diameter of the circle, show that triangle APB is equilateral.

PQ and QT are tangents to a circle with centre O. If OPQ is an isosceles triangle .Then fing angle PQT.

If a, b, c are the sides of a right triangle where c is the hypotenuse, then prove that radius r of the circle touches the sides of the triangle is given by r = a+b+c/2

one circle has radius 5 and its centre (0,5). A second circle has radius of 12 and its centre (12,0). What is the length of the radius of a third circle which passes through the centre of the second circle and both the points of intersection of the first two circles.

Two tangent segments PA and PB are drawn to a circle with centre O, such that angle APB= 120degree. Prove that OP=2AP.

ABCD is a quadrilateral such that angle D=90degree. A circle with centre O and radius r touches the sides AB,BC,CD and DA at P,Q,R and S respectively. If BC=38 cmCD=25cm and BP=27 cm find r

IF ANGLE BETWEEN TWO TANGENTS DRAWN FROM A POINT P TO A CIRCLE OF RADIUS A AND CENTER O IS 60 DEGREE THEN PROVE THAT AP = A UNDER ROOT 3.

Two circles intersect each other at points P and Q. If AB and AC are the tangents to the circles from a point A on QP produced show that AB=AC

Reply as fast as possible please

prove that the tangents drawn at ends of a diameter of a circle are parallel.

The ratio of the sums to first n terms of two APs is (3n+1):(5n+8). Find the ratio of their 13th terms.

From an external point P, two tangents PA and PB are drawn to a circle

Circles C (O,r) and C(O', r'), (r r' ) touch internally at P. PQ is a chord of circle C (O,r) which intersect circle C (O' , r' ) at R. Show that OO'RQ is a Trapezium.

Prove that the parallelogram circumscribing a circle is a rhombus. in this question do also have to prove that the diagonals are also equal?

^{0}two circles with centres O and O' of radii 3cm and 4cm respectively intersect at two points P and Q such that OP and O'P are tangents to the two circles find the lenghth of the common chord PQ.

how many parallel tangents can a circle have?

A circle touches all the four sides of a quadrilateral ABCD whose sides are AB = 6 cm , BC = 7 cm and CD = 4 cm. Find AD.

if from any point on the common chord of two intersecting circles , tangents be drawn to the circles , prove that they are equal .

PQ and PT are tangents drwan from a point P to a circle with centre O such that angle QPT=120 then angle QOT is equal to??

PQ and RS are two parallel tangents to a circle with centre'O',another tangent AB with the point of contact 'C' intersecting PQ and RS at A and B respectively.Prove that angle AOB=90 degree.

_{1},d_{2}(d_{2}>d_{1}) be the diameter of the two concentric circles and 'c' be the length of a chord of circle which is tangent to the other circle.Prove that d_{2}^{2 }= c^{2}+ d_{1}^{2}.....[1]If PA and PB are tangents from an outside point P such that PA = 10 cm and angle APB = 60 .find the length of the chord AB.

[2]prove that the tangent drawn at the ends of a chord of a circle make equal with the chord.

[3]prove that the line segment joining the points of contact of two parallel tangent to a circle is a diameter of the circle.

The radius of the incircle of a triangle is 4 cm and the segments into which one side is divided by the point of contact are 6cm and 8 cm .Determine the other two sides of the triangle.(A) 13 cm

(B) 15 cm

(C) 11 cm

(D) 10 cm

Two circles touch externally at a point P and a common tangent touches them at A and B.Prove that AB subtends a right angle at P.

ACTIVITY:-TO find the area of a circle by paper cutting and pasting method. (in 2000-3000 words)

pz...... give the necessary details with diagram or by drawings.

(i)RA=SB

(ii)RS²=P'P² AB²

I AM ASKING THIS THIS QUESTION SECOND TIME I HAV NOT GOT THE WAY HOW THEY DID .....

AND I REQUEST THE EXPERTS NOT TO CLOSE THE CONVERSATION .. I WANT TO ASK SOME DOUBTS......PLZ...🙏

Tangents PQ and PR are drawn to a circle such that angle RPQ= 30 degreeA chord RS is drawn parallel to tangent PQ.

Find angle RQS...??? ANSFAST...

ab and cd are common tangents to two circles of unequal radii. prove that ab=cd

From a point P, two tangents PA and PB are drawn to a circle with centre O. If OP = diameter of the circle, show that the triangle APB is equilateral.

(A) PQ = 13 cm

(B) PQ = 10 cm

(C) RS = 13 cm

(D) area of trapezium RSCD is 78 $c{m}^{2}$

In a right triangle ABC in which angle B = 90', a circle is drawn with AB as diameter intersecting the hypotenuse ACat P. Prove that the tangent to the circle at P visects BC.

in two concentric circles, prove that all chords of the outer circle which touches the inner circle are of equal lengths.

prove that the parallelogram circumscribing a circle is a rhombus.???

PAB is a secant and PT is a tangent. Prove that PA X PB =PT^{2}please tell me how to find cgpa?

the difference of squares of two numbers is 180. the square of smaller no. is 8 times the larger number. find the two numbers .

The sides AB,BC,CA of triangle ABC touch a circle with centre o and radius r at P,Q,R respectively.Prove that

(1) AB+CQ= AC+BQ

(2) Area (triangle ABC) = 1/2 (perimeter of triangle ABC) x r (radius)

^{o}.A circle is inscribed in a triangle ABC, having sides 8 cm , 10 cm and 12 cm. Find AD , BE and CF ( these 3 are altitudes of triangle ABC).

Triangle ABC is isosceles in which AB=AC circumscribed about a circle. Prove that base is bisected by the point of contact.

in two concentric circles, prove that all chords of the outer circle which touches the inner circle are of equal lengths.

quadrilateral ABCD is circumscribed to a circle with centre o.if angle AOB = 115, then angle cod is?

Equal circles with centres O and O' touch each other at X. OO' produced to meet a circle with centre O , at A. AC is a tangent to the circle whose centre is O. O'D is perpendicular to AC. Find the value of DO'/CO.....cAn aNy1 hElP MeH WiD thIs qUeStIoN pLs...???????

If from a external point P of a circle with centre O, two tangents PQ and PRare drawn such that angle of QPR=120. prove tht 2PQ=PO.

The tangent at pt C of a circle and a diameter AB when extended intersect at P.If angle PCA = 110 find angle CBA

Q17. In the given figure, PYA, PZB XMW and YNZ are the tangents to the circle with centre O. If the ratio of the perimeters of $\u2206$ PYZ and $\u2206$PXW is p : q and XM =WM, then the raio of PY to PX is equal to

(A) 2p : q – p (B) 2p : q + p

(C) 2q : q – p (D) 2q : q + p

Q1) From an external point P, tangents PA and PB are drawn to a circle with cente O.If CD is the tangent to the circle at a point E and PA=14cm, find the perimeter of triangle PCD.

Q2) a circle touches all the four sides of a quadrilateral ABCD whose three sides are AB=6cm, BC=7cm, and CD=4cm find AD.

if possible u pls. explain me these sums through video.

Solve fast..

A boy is cycling such that the wheels of the cycle are making 140 revolutions per minute. If

prove that line segment joining the points of contact of two parallel tangents is the diameter of the circle

Prove that the angle between two tangents drawn from an external point to a circle is

supplementary to the angle subtended by the line segment joining the points of contact at the centre.

three spheres are kept inside a cone. spheres are touching both the slant sides of the cone and the adjacent spheres. if the radiusof the 1st sphere and the 3rd sphere are 5 units and 20units resp. find the radius of the 2nd sphere?

PQL and PRM are tangents to the circle with centre o at the points Q and R ,respectively and S is a point on the circle such that angle SQL=50 and angle SRM=60. Find angle QSR.

The tangent at a point C of a circle and diameter AB when extended intersect at P. If PCA=1100 , find CBA.6. The tangent at a point C of a circle and diameter AB when extended intersect at P. If PCA=1100 , find CBA.

AB is line segment of length 24 cm. C is its midpoint. On AB, AC and BC semicircles are described. Find the radius of the circle which touches all the three semicircles.