Chapter 6.4, Problem 11E

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6th Edition

Daniel C. Alexander + 1 other

ISBN: 9781285195698

Textbook Problem

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To determine

**To find:**

If the given two triangles are similar or not.

Explanation

**Given:**

A circle

**Postulate:**

The measure of an inscribed angle of a circle is half the measure of its intercepted arc. Consider the figure below, let the inscribed angle be

Then

The measure of the angle formed by intersecting tangents is given by half the positive difference of the measures of the intercepted arcs.

Consider the figure below, let the inscribed angle be

Then

**Calculation:**

Since, the measure of an inscribed angle of a circle is half the measure of its intercepted arc therefore from the figure given,

We get,

Substituting

Similarly,

Substituting

Similarly,

Substituting

Since, the measure of the angle formed by intersecting tangents is given by half the positive difference of the measures of the intercepted arcs therefore from the figure given, we get

The arc

Substituting

Substituting

Simplifying,

Similarly,

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