Find the area of a square inscribed in a circle of radius $a$

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Solution

$R a d i u s$ $= a$ & $D i a m e t e r$ $= 2 a$
$D i a g o n a l o f s q u a r e$ $= 2 a$
$A C^{2} = A B^{2} + B C^{2}$
$(2 a)^{2} = (s i d e)^{2} + (s i d e)^{2}$
$4 a^{2} = 2 s i d e^{2}$
$s i d e^{2} = \frac{4 a^{2}}{2} = 2 a^{2}$
$A r e a o f s q u a r e$ $= s i d e^{2} = 2 a^{2}$

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