   Chapter 6.CR, Problem 31CR ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# A square is inscribed in a circle with a radius of length 6 cm. Find the perimeter of the square.

To determine

To Find: The perimeter of the square if it is inscribed in a circle with radius of length 6 cm.

Explanation

Concept:

Definition:

A central angle of a circle is an angle whose vertex is the center of the circle and whose sides are radii of the circle.

Definition:

An inscribed angle of a circle is an angle whose vertex is a point on the circle and whose sides are chords of the circle.

Theorem 6.1.2:

The measure of an inscribed angle of a circle is one-half the measure of its intercepted arc.

Theorem 6.1.8:

Congruent chords are located at the same distance from the center of a circle.

Theorem 6.1.9:

Angle inscribed in a semicircle is a right angle.

Calculation:

Given that a square is inscribed in O with radius of length 6 cm.

By Theorem 6.1.9:

Angle inscribed in a semicircle is a right angle.

If a square is inscribed in a circle, then its diagonals are diameters of the circle.

Let A,B, C and D be vertices of the square.

Then AC and BD are the diagonals of the square and the diameters of the circle.

AB,BC, CD and DA are the sides of the square.

Then AOB, BOC, COD, AOD are right triangles

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