Chapter 6.3, Problem 10E

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6th Edition

Daniel C. Alexander + 1 other

ISBN: 9781285195698

Textbook Problem

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*In the figure for Exercises 7 to 16, O is the center of the circle. See Theorem 6.3.5.*

*Given:*

*Find: DE *and* EC.*

To determine

**To find:**

The values of *DE* and *EC*

Explanation

Given that

The diagrammatic representation is given below,

**Theorem:**

If two chords intersect within a circle, then the product of the lengths of the segments (parts) of one chord is equal to the product of the lengths of the segments of the other chord.

By using the theorem to get the following,

Also, know that

Substitute the values

Substitute equation (3) in equation (4) to get the following,

Solve the above quadratic equation to get the following,

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