Chapter 6.1, Problem 19E

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7th Edition

Alexander + 2 others

ISBN: 9781337614085

Textbook Problem

Circles

*Exercises 18, 19*

To determine

**To find:**

The length of

Explanation

**Given:**

Circles *O* and *Q* have the common chord *O* has a radius of length 4 and the circle with center *Q* has a radius of length 6. The length of *AB *is 6.

**Theorem used:**

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

An angle inscribed in a semicircle is a right angle.

Segment addition postulate:

If *X* is a point on *A-X-B*, then

**Calculation:**

In the circle *O*, *Q*,

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

Hence

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

Consider,

Since

In right

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