In fig., a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively, If AB = 29 cm, AD = 23 cm, $∠$ B = 90^o and DS = 5 cm, then the radius of thecircle (in cm) is

11

18

6

15

Solution

Given: Ab, BC,CD,and AD tangents to the circle with centre O at

Q,P,S and R respectively.

AB=29 cm, AD=23 cm, DS=5 cm and $∠$ B=90⁰

Construction: Join PQ.

We know that, the lengths of the tangents drawn from an external

point to a circle are equal.

DS=DR=5 cm

$∴$ AR= AD - DR= 23 cm- 5 cm= 18 cm

AQ=AR= 18 cm

$∴$ QB = AB - AQ = 29 cm - 18 cm= 11 cm

QB = BP = 11 cm

In $∆$ $In ∆ PQB {PQ}^{2} = {QB}^{2} + {BP}^{2} = (11 cm)^{2} + (11 cm)^{2} = 2 x (11 cm)^{2} PQ = 11 \sqrt{2} cm . . . . . . . . . . (1) IN ∆ OPQ, {PQ}^{2} = {OQ}^{2} + {OP}^{2} = r^{2} + r^{2} = 2 {r^{2}}^{} (11 \sqrt{2})^{2} = 2 {r^{2}}^{} 121 = r^{2} r = 11 cm Thus, the radius of the circleis 11 cm .$

For Daily Free Study Material Join wiredfaculty

Circles

In fig., a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively, If AB = 29 cm, AD = 23 cm, $∠$ B = 90^o and DS = 5 cm, then the radius of thecircle (in cm) is

11

18

6

15

Some More Questions From Circles Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction

For Daily Free Study Material Join wiredfaculty

Circles

In fig., a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively, If AB = 29 cm, AD = 23 cm, ∠B = 90o and DS = 5 cm, then the radius of thecircle (in cm) is 11 18 6 15

Some More Questions From Circles Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

In fig., a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively, If AB = 29 cm, AD = 23 cm, $∠$ B = 90^o and DS = 5 cm, then the radius of thecircle (in cm) is

11

18

6

15