Chapter 6.CR, Problem 4CR

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7th Edition

Alexander + 2 others

ISBN: 9781337614085

Textbook Problem

Two circles intersect and have a common chord 12 cm long. The measure of the angles formed by the common chord and a radius of each circle to the points of intersection of the circles is

To determine

**To find:** The radius length of each.

Explanation

**Theorem:**

1) A radius that is perpendicular to a chord bisects the chord.

2) If a line through the centre of a circle bisects a chord other than a diameter, then it is perpendicular to the chord.

**Calculation:**

Let the centers of the two circles be A and B.

And also let the common chord be PQ.

Given that the length of common chord = PQ = 12 cm.

The distance between the centers of the circles = AB.

Let the radius of the circle with center A = PA =

Also, the measure of the angles formed by the common chord and a radius of each circle to the points of intersection of the circles is

So,

But,

So, â—¿

By theorem,

So, â—¿

Since

So, AO = PO and PO = OB

So, â—¿

So, â—¿

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