Chapter 6.4, Problem 31E

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6th Edition

Daniel C. Alexander + 1 other

ISBN: 9781285195698

Textbook Problem

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Circle

To determine

**To find:**

The distance that

Explanation

**Given:**

Circle

**Theorem Used:**

According to the Pythagorean theorem, in a right-angled triangle,

hypotenuse^{2 }= base^{2 }+ perpendicular^{2}.

**Property Used:**

If two sides of a triangle are equal then the angles formed by the legs of the included angle are also equal.

The sum of all the angles of a triangle is

An equilateral triangle has all the angles and all the sides equal.

The perpendicular bisector divides the chord into two equal parts.

**Approach:**

i) Find the length of the chords,

ii) Use the Pythagorean theorem to calculate the distance of chords from center (i.e.)

iii) Find the difference between,

**Calculation:**

The central angles equals

In the given figure,

Let

Applying Pythagorean theorem, in

hypotenuse^{2}=base^{2}+perpendicular^{2}.

Substituting

In

Since, the sum of all the angles of a triangle is

Since,

Thus,

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