Chapter 6.CR, Problem 31CR

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7th Edition

Alexander + 2 others

ISBN: 9781337614085

Textbook Problem

**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

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

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

So, radiii =

Then

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