   Chapter 6.4, Problem 19E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Given circle O with radius O T ¯ , tangent A D ↔ , and the line segments O A ¯ , O B ¯ , O C ¯ , and O D ¯ :a) Which line segment drawn from O has the shortest length?b) If m ∠ 1 = 40 ° , m ∠ 2 = 50 ° , m ∠ 3 = 45 ° , and m ∠ 4 = 30 ° , which line segment from point O has the greatest length? To determine

(a)

To find:

The line segment drawn from center that has the shortest length.

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, QT is a tangent to O at point T.

The perpendicular distance is the shortest distance between two points or lines.

Given:

The circle O with radius OT¯, tangent AD, and the line segments OA¯, OB¯

To determine

(b)

To find:

The line segment drawn from center that has the greatest length.

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