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Question
In the below fig. OCDE is a rectangle inscribed in a quadrant of a circle of radius 10 cm. If
OE = 2√5, find the area of the rectangle.
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Solution
Given OD = 10cm and OE `root (2)(5)cm`
By using Pythagoras theorem
∴ `OD^2 = OE^2 + DE^2`
⇒ `DE = sqrt( OD^2 - OF^2)` = ` sqrt (( 10 )^2 - (root2(5)))^2` = `root 4 (5)cm`
∴ `ar (rect DCDE) = OExx DE = root2( 5) xx root 4 (5 )cm^2`
= `40 cm^ 2 [ ∴ sqrt5 xx sqrt 5 = 5]`
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