Chapter 14.6, Problem 24PSE

To determine

To construct a circle that is tangent to the sides of the angle and passes through the given point.

Explanation of Solution

Given:

The acute angle with a point P in the interior of the angle.

Calculation:

The equilateral triangle whose area is equal to that of hexagon can be constructed as follows-

Step 1- First draw the acute angle ABC with a point P in its interior.

Step 2- Now draw the circle taking the point P as center.

Step 3- Now, draw the three circles and one big circle as shown in the figure below.

Step 4- These areas can be equal when

Step 5- After completing the intersection, it can be seen that there are two circles which can act as tangent to the given angle.

Step 6- The bigger circle is the required circle.