Chapter 14, Problem 17RP

To determine

To find the locus of the midpoints of all chords of a circle that have a fixed point of the circle as an end point.

Answer to Problem 17RP

A circle that has a diameter same as the radius of the original circle and touches the original circle internally at one point which is the fixed end point of all the chords.

Explanation of Solution

Given:

The circle with chords.

Calculation:

The locus of the midpoints of all chords of a circle that have a fixed point of the circle as an end point will be a circle that has a diameter same as the radius of the original circle and touches the original circle internally at one point which is the fixed end point of all the chords.