Question

Draw a square whose vertices lie on a circle of radius 5 cm. Find the ratio of the areas of the square and the circle.​

Answer 1

Answer:

Step-by-step explanation:

Squares Circumscribed by Circles

When a square is circumscribed by a circle , the diagonal of the square is equal to the diameter of the circle.

Example 1:

Find the side length s of the square.

The diagonal of the square is 3 inches. We know from the Pythagorean Theorem that the diagonal of a square is 2√ times the length of a side. Therefore:

s2√=3s=32√=32√2  in.

 

Example 2:

Find the area of the circle.

First, find the diagonal of the square. Its length is 2√ times the length of the side, or 52√ cm.

This value is also the diameter of the circle. So, the radius of the circle is half that length, or 52√2 .

To find the area of the circle, use the formula A=πr2 .

A=π(52√2)2=π(25⋅24)=252π  cm2

Answer 2

Answer:

• Draw a square whose vertices lie on a circle of radius 5 cm. Find the ratio of the areas of the square and the circle.

Step-by-step explanation:

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