Chapter 6.3, Problem 12E

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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: EC.*

To determine

**To find:**

The value of *EC*.

Explanation

Given that

The diagrammatic representation is given below,

**Theorem:**

1. 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. Now compare the triangles

2. If two inscribed angles intercept the same arc, then these angles congruent. By using the above theorem

**Vertical angles** are congruent to each other. The **angles** that are opposite to each other are **vertical angles**.

By suing the vertical angle theorem to get the following,

Since by Angle rule we conclude that

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