   Chapter 8.3, Problem 33E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Find the ratio of the area of a square circumscribed about a circle to the area of a square inscribed in the circle.

To determine

To find:

The ratio of the area of a square circumscribed about a circle to the area of a square inscribed in the circle.

Explanation

The area of the square is given by, A = s2 where s is side of the square.

Calculation:

Consider a circle with center O, ABCD as circumscribed square and PQRS as inscribed square.

Let us suppose the side of the PQRS be x, i.e., PQ = QR = RS = SP = x

Since, PQRS as inscribed square and all the angles of a square are right angles.

Hence, QPS=90

Use Pythagoras theorem in ΔPQS.

QS2=PQ2+PS2QS2=x2+x2QS2=2x2

The diameter of the circle is equal to the side AD of the circumscribed square

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