Chapter 6.4, Problem 15E

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7th Edition

Alexander + 2 others

ISBN: 9781337614085

Textbook Problem

Point

To determine

**To construct:**

Two tangent segments to a circle from an external point and determine the measure of the angle that has vertex as the external point and tangents as sides.

Explanation

The line that is perpendicular to the radius of a circle at its endpoint on the circle is a tangent to the circle. In the given figure,

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 central angle formed by two radii,

It is given by

The angle formed by radius drawn to tangent equals

**Given:**

The circle

**Construction Strategy:**

i) Draw a circle

ii) Take an external point

iii) Construct the perpendicular bisector of line

iv) With

**Construction:**

Constructing a circle

Constructing the perpendicular bisector of line

Now with

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