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.

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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????

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 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

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

1. AQ = 1/2 ( perimeter of triangle ABC)

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

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

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

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

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?

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

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

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.

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

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

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.

 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 degree
A 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.

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.

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

PAB is a secant and PT is a tangent. Prove that PA X PB =PT²

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)

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.

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.

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.

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

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.

 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.