Chapter 6.3, Problem 46E

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7th Edition

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Textbook Problem

*In Exercises 46 to 49, prove the stated theorem.*

If a line is drawn through the center of a circle perpendicular to a chord, then it bisects the chord and its minor arc. See Figure 6.37 on page 298.

*(NOTE: The major arc is also bisected by the line.)*

To determine

**To find:**

To prove the following stated theorem,

“If a line is drawn through the center of a circle perpendicular to a chord, then it bisects the chord and its minor arc”.

Explanation

Given that

To prove

The diagrammatic representation is given below,

Since

Then *AC, AD* be the radius of the circle. Therefore,

We know that angles which are opposite to equal sides are also equal.

Therefore

Also,

By using AAS congruence rule ( that is any two angle of one triangle is congruent to corresponding two angles of the other triangles and one side of the one triangle is congruent to the corresponding side of the other triangles then these triangles are congruent)

Using the CPCTC (corresponding parts of congruent triangles are congruent) to get the following,

Consider the

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