Chapter 6.1, Problem 18E

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7th Edition

Alexander + 2 others

ISBN: 9781337614085

Textbook Problem

**common chord** of

*Exercises 18, 19*

To determine

**To calculate:**

The length of

Explanation

**Given:**

**Theorem used:**

1. A radius that is perpendicular to the chord bisects the chord.

2. An angle inscribed in a semicircle is a right angle.

**Calculation:**

In the circle *O*, *Q*,

Thus *AQBO* is a rhombus with diagonals

We know that the diagonals of a rhombus are perpendicular to each other.

Hence

By the theorem, “A radius that is perpendicular to the chord bisects the chord”, we get

Consider,

Since

Now consider two triangles

Here,

Since, the two triangles are congruent, we get

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