24. The ratio of the area of circle with centre O and the area of the rectangle ABCD inscribed in it is π :\sqrt{}3 . E is a point on AB such that ∠ADE = ∠ODC. Find AE :AD.

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Q. In the figure above (not drawn to scale), rectangle ABCD is inscribed in the circle with centre at O. The length of side AB is greater than that of side BC. The ratio of the area of the circle to the area of the rectangle ABCD is

π : \sqrt{3} .

The line segment DE interests AB at E such that

∠ O D C = ∠ A D E

What is the ratio AE : AD?

Q. In the figure below

(n o t d r a w n t o s c a l e), r e c t a n g l e

ABCD

i s i n s c r i b e d i n t h e c i r c l e w i t h c e n t r e o f O . T h e l e n g t h o f s i d e

i s g r e a t e r t h a n t h a t o f s i d e

. T h e r a t i o o f t h e a r e a o f t h e c i r c l e t o t h e r e c t a n g l e

ABCD

i s

\pi : \sqrt {3}

. T h e l i n e s e g m e n t

i n t e r s e c t s

a t E s u c h t h a t

\angle ODC = \angle ADE

. W h a t i s t h e r a t i o

AE : AD$?

In the given figure, 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, $∠$ = $90^{o}$ and DS = 5 cm then find the radius of the circle.

Q. In the given figure, a circle with centre O, is inscribed in a quadrilateral ABCD such that it touches the side BC, AB, AD and CD at points P, Q, R and S respectively. If AB = 29 cm, AD = 23 cm, ∠B = 90^∘ and DS = 5 cm then find the radius of the circle. [CBSE 2008, 13]

Q. In fig. 2, 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

A B = 29 c m, A D = 23

∠ B = 90^{\circ}

and

D S = 5 c m

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

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