Chapter 6.1, Problem 40E

### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

Chapter
Section

### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# Use a paragraph proof to complete this exercise. Given: âŠ™ O with chords A B Â¯ and B C Â¯ , radii A O Â¯ and O C Â¯ Prove: m âˆ  A B C < m âˆ  A O C

To determine

To prove:

In a circle with centre O, AB¯ and BC¯ are the chords and AO¯,OC¯ are radii, then mABC<mAOC.

Explanation

Given:

In a circle with centre O, ABÂ¯ and BCÂ¯ are the chords and AOÂ¯,OCÂ¯ are radii.

Theorem used:

The measure of an inscribed angle of a circle is one-half the measure of its intercepted arc.

Central angle postulate:

In a circle, the degree measure of a central angle is equal to the degree measure of its intercepted arc.

Proof:

Consider a circle with center O.

Let ABÂ¯ and BCÂ¯ be the chords and let AOÂ¯,OCÂ¯ be radii of the circle.

From the figure, we see that âˆ AOC is the central angle.

By central angle postulate, mâˆ AOC=mACâŒ¢.

From the figure we see that âˆ ABC is the inscribed angle with the intercepted arc ACâŒ¢

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