Chapter 14, Problem 28RP

To determine

To construct a circle in the exterior of the triangle whose side is tangent to the circle.

Answer to Problem 28RP

The point where the perpendicular bisector meets the two circles is the locus.

Explanation of Solution

Given:

A scalene triangle ABC.

Calculation:

A circle in the exterior of the triangle whose side is tangent to the circle can be constructed as follows-

Draw an angle bisector of the angle opposite to the side that will be tangent to the circle. From the angle bisector choose an appropriate exterior point and drop a perpendicular on the side that is supposed to be a tangent. The length of the perpendicular is the radius of the circle, using the previous point as the center draw the circle.