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In the following figure, $O C D E$ is a rectangle inscribed in a quadrilateral of a circle of radius $10$ is a rectangle inscribed in a quadrilateral of a circle of radius cm. If $O E = 25 c m$ cm. If , then the area of the rectangle from the options given below is:

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10 cm 2

20 cm 2

30 cm 2

40 cm 2

answer is D.

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Detailed Solution

Given that,

O E = 25 c m

.
The radius of the circle, OD = 10 cm. Question Image

From the figure,

D E

is perpendicular to

E O

.
By Pythagoras theorem in the right triangle OED,

(h y p o t e n u s e) 2 = (b a s e) 2 + (p e r p e n d i c u l a r) 2

O D 2 = O E 2 + D E 2

⇒ (10) 2 = (25) 2 + D E 2

⇒ D E 2 = 100 − 20

⇒ D E = 80

⇒ D E = 45 c m

Area of the rectangle

= l e n g t h × b r e a d t h

Area of a rectangle OCDE

= O E × D F

Area of a rectangle OCDE

= 25 × 45

= 8 × 5

= 40 c m 2

The area of the rectangle OCDE is

40 c m 2

.
Hence option 4) is correct.

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