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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

Q17. An isosceles trapezium ABCD is inscribed in a semicircle with centre 'O' and diameter AD as shown. If AD = 2a and AB = b then the length BC is equal to.

(A) (2a

^{2}– b^{2}) / a (B) 2 (a^{2}– b^{2})/a (C) $\surd $(2a^{2}– b^{2}) (D) 2$\surd $(2a^{}^{2}– b^{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.

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

If the angle between two radii of a circle is 140 DEGREE, then the angle between the tangets at the ends of the radii is ?

prove 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

the adjacent sides AB,BC OF A SQUARE OF SIDES "a" units are tangent to a circle . the vertex D of the square lies on the cirumference of the circle . what will be the radius of the circle ?

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?

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

AB is a chord of length 9.6cm of a circle with centre O and radius 6 cm. If the tangents at A and B intersect at point P then find the length 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.

Two rays ABP and ACQ are intersected by two parallel lines in B, C and P, Q respectively. Prove that the circumcircle of Δ ABC and Δ APQ touch each other at A.

(Hint: Draw tangent XAY to the circumcircle of triangle APQ and show that ∠ YAP = ∠PQA = ∠ BCA)

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

IT IS THE QUESTION OF CIRCLES MAM/SIR

let P be any point on the circumcircle of triangle ABC and perpendiculars PL ,PM ,PN are drawn on the lines through line segment BC CA and AB respectively shhow that the points L M N are collinear this LMN line is called as Simpsons line

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

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

In the given figure, BC is the diameter of the circle with the centre O and PAT is the tangent at A. IfÐABC = 38

^{o}, findÐBAT. No figure though.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?

chapter 10.2 Qno 12

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

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.

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

A triangle ABC is drawn to circumscribe a circle of radius 10cm such that the segments BP and PC into which BC is divided by the point of contact P ,are of lengths 15 cm and 20cm respectively . If the are of triangle ABC = 525 cm sq , then find the lenghts of AB and AC

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

a)3.5 cm

b)5.5 cm

c)7.5 cm

d)12.5 cm

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.

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

each other externally. A third circle with centre R is drawn to touch the first two circles and

one of their common internal tangents as shown in the figure.Then,the radius of the circle with centre R is

The tangents TP and TQ are drawn to a cicle with centre O, from an external point T. Prove that Angle PTQ= 2 of angle OPQ

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

AT is a tangent to the circle with centre O such that OT=4cm and <OTA=30degree the AT is equal to

A)4cm

B)2cm

C)2root3cm

D)4root3cm

Pls explain briefly

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

Plsss explain me sum no. 12 ...chapter no.10 ...ex.10.2

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.

Q11Prove that the line segment joining the points of contact of two parallel tangents of a circle, passes through its centre.EXPERTS I AM NOT SATISFIED WITH THE PROVIDED SOLUTION IN SOLVED BOARD PAPER OF MATHS 2014. PLEASE CAN I GET AN ALTERNATIVE SOLUTION FOR THIS QUESTION???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 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]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.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.

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

EXPERTS PLEASE TELL THAT :

WHAT IS THE SECANT OF THE CIRCLE ??

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.

Circles are drawn from 3 vertices of a triangle ABC taken as centre to touch each other externally. the sides of the triangle are 4cm, 6cm, 8cm. find the radii of the circles

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.

"PP' and QQ'are two direct common tangents to circle to two circles with centre O and O'intersecting at A ad B .The common chord AB on producing meets the tangents PP'at R and QQ' at S .Show that RS

^{2}=PP'^{2}+AB^{2}. "prove that the parallelogram circumscribing a circle is a rhombus.???

Let PT be a tangent to the circle from an external point P and a secant to the circle through P intersects the circle at points A and B, then PT

^{2}= PA � PB”.I am unable to understand this line plese explain.............. ask the expert

PAB is a secant and PT is a tangent. Prove that PA X PB =PT^{2}in a triangle abc the incircle touches the sides bc,ca and ab respectively at d,e and f.if the radius of the incircle is 4units and if bd,ce and af are consecutive integers,find the sides of triangle abc

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

from an external point p, two tangent pa and pb are drawn to the circle with centre o. if c is midpoint of cord ab prove that pc passes through the centre o of the circle

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)

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.

(A) a+b (B) 2(a+b) (C) √2(a+b) (D) 2√ab

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

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...???????

(A) 324 π (B) 81 π (C) 1296 π (D) 162 π

(E) Cannot be determined from given information

9. The figure in the diagram is formed by two overlapping circles. The circles have radii 1 and 3 respectively. If the area of the shaded region is $\frac{\pi}{2}$, then the total area of the figure is

(A) 10 π (B) $\frac{19\mathrm{\pi}}{2}$ (C) 8 π (D) $\frac{7\mathrm{\pi}}{2}$ (E) 9 π

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

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.

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

a chord of a circle of diameter 24cm subtends angle of 60 degree at the centre of the circle .find the area of the corresponding [a] minor sector [b] minor segment

plzzz plzz plzz help[;(

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.

in ,triangle pqr,angle Q=90,A CIRCLE WITH CENTRE O AND RADIUS 2 CM HAS BEEN INSCRIBED IN THE TRIANGLE.IF QR=6 CM ,FIND THE PERIMETER OF TRIANGLE PQR

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.

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

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.

The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.