Question 170537: A square is inscribed in a circle whose diameter is 10 cm. Find the length of the side of the square.
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! A square is inscribed in a circle whose diameter is 10 cm. Find the length of the side of the square.
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The diagonal of the square is the diameter of the circle, = 10 cm.
The diagonal makes a 45 deg angle with the side, so the side is 10*sin(45)
= 5*sqrt(2) cm =~7.07 cm
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Using Pythagoras, the 2 sides are equal, so
d^2 = a^2 + a^2 (diagonal d, sides a)
100 = 2a^2
a = sqrt(50) = 5*sqrt(2) same answer.
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