Chapter 6.1, Problem 35E

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7th Edition

Alexander + 2 others

ISBN: 9781337614085

Textbook Problem

*In Exercises 32 to 37, write a paragraph proof.*

A radius perpendicular to a chord bisects the arc of that chord.

To determine

**To prove:**

The statement “A radius perpendicular to the chord bisects the arc of that chord”.

Explanation

**Given:**

The provided statement is “A radius perpendicular to the chord bisects the arc of that chord”.

**Theorem used:**

*Hypotenuse Leg theorem:*

If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and the leg of a second right triangle, then the triangles are congruent.

**Proof:**

Consider a circle with center *O.* Let

We have to prove the radius perpendicular to the chord bisects the arc of that chord. That is to prove

Draw radii

Consider the triangles *OCA *and *OCB*.

Since the radii of the circle are equal, we can say

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