Chapter 14, Problem 30RP

To determine

To construct a circle that is tangent to both the lines and passes through the point.

Answer to Problem 30RP

Measure the distance between the two parallel lines.

Explanation of Solution

Given:

The two parallel lines and a point P.

Calculation:

A circle that is tangent to both the lines and passes through the point can be constructed as follows-

Draw a parallel line equidistant from both of them. Measure the distance between the two parallel lines, divide it by $2$ , and then use it to cut an arc on this new line from P. The intersection is the center of the circle. Draw the circle with the parallel lines being the tangent and P being a point on it.