In the given figure, a circle is inscribed in a quadrilateral ABCD in which $∠ B = 90$ . If AD =23 cm, and AB=29 cm and DS = 5 cm, find the radius r of the circle.

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Solution

From figure,
$D S = D R$ , $A R = A Q$ , $B P = B Q$ (Tangent property)

$A R = A Q = A D - D R = A Q$

$∴ A D - D S = A Q = (23 - 5) c m = 18 c m$ ........... $(D R = D S)$

$B P = A B - A Q = 29 - 18 c m = 11 c m$

$∴ B P = B Q = 11 c m$

As, $∠ B = 90^{0}$ So, $O Q = B P = Q B = O P = 11 c m$

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In the given figure, a circle is inscribed in a quadrilateral ABCD in which ∠B=90. If AD =23 cm, and AB=29 cm and DS = 5 cm, find the radius r of the circle.

From figure,DS=DR, AR=AQ, BP=BQ (Tangent property)AR=AQ=AD−DR=AQ∴AD−DS=AQ=(23−5)cm=18cm ...........(DR=DS)BP=AB−AQ=29−18cm=11cm∴BP=BQ=11cmAs, ∠B=900 So, OQ=BP=QB=OP=11cm

In the given figure, a circle is inscribed in a quadrilateral ABCD in which $∠ B = 90$ . If AD =23 cm, and AB=29 cm and DS = 5 cm, find the radius r of the circle.