A square is placed in a circle of area (49π)cm^2 such that all four vertices of the square lie on the circumference of the circle. What is the area of the square?

It's always helpful to draw a diagram beforehand.Since we know the area of the circle is (49π)cm2, we can work out the radius using A=πr2 . Rearranging, we get r = 7cm. Add this information to our diagram. We can see the diameter of the circle is a diagonal of the square.This means we can use the Pythagorean Theorem to find the side of the square. Let the side of the square = x cm Diameter= 2* radius = 14 cmFrom the Pythagorean Theorem: x2 + x2 = 142 2x2=196 x2=98We are trying to find the area of the square, which is the (side length of the square)2, which in this case is 98. Therefore, the answer is 98cm2

Answered by Karnan S. Maths tutor

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