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In fig., a circle with centre O is inscribed in a quadrilatera

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In fig., a circle with centre $O$ is inscribed in a quadrilateral $A BC D$ such that, it touches the sides $BC, A B, A D$ and $C D$ at points $P, Q, R$ and $S$ respectively, If $A B = 29$ cm, $A D = 23$ cm, $∠ B = 9 0^{o}$ and $D S = 5$ cm, then the radius of the circle (in cm) is:

11

18

6

15

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In fig., a circle with centre

O

is inscribed in a quadrilateral

A BC D

such that, it touches the sides

BC, A B, A D

and

C D

at points

P, Q, R

and

S

respectively, If

A B = 29

cm,

A D = 23

cm,

∠ B = 9 0^{o}

and

D S = 5

cm, then the radius of the circle (in cm) is:

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Text solutionVerified

Given : A quadrilateral

A BC D

in which

∠ B = 9 0^{0}

and

A D = 23 c m, A B = 29 c m

and

D S = 5 c m

Then,

D R = D S = 5 c m

A D = 23 c m

A R + R D = 23 c m

A R + 5 = 23 c m

A R = 23-5 = 18 c m

A Q = A R

[Tangents from an external point]

A R = 18 c m

Therefore,

A Q = 18 c m

A Q + QB = 29 c m

18 + QB = 29 c m

QB = 11 c m

∴ OP

and

OQ

are radii of the circle.

From tangents

P

and

Q

∠ OPB = ∠ OQB = 9 0^{0}

Now

OPBQ

is a square.

∴ OP = BQ

Radius

(r) = 11 c m

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Question Text	In fig., a circle with centre $O$ is inscribed in a quadrilateral $A BC D$ such that, it touches the sides $BC, A B, A D$ and $C D$ at points $P, Q, R$ and $S$ respectively, If $A B = 29$ cm, $A D = 23$ cm, $∠ B = 9 0^{o}$ and $D S = 5$ cm, then the radius of the circle (in cm) is:
Answer Type	Text solution:1
Upvotes	150

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 the circle (in cm) is:

Text solutionVerified

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In fig., a circle with centre $O$ is inscribed in a quadrilateral $A BC D$ such that, it touches the sides $BC, A B, A D$ and $C D$ at points $P, Q, R$ and $S$ respectively, If $A B = 29$ cm, $A D = 23$ cm, $∠ B = 9 0^{o}$ and $D S = 5$ cm, then the radius of the circle (in cm) is: