Chapter 14, Problem 3CTE

To determine

To construct: s large triangle and inscribe a circle within it.

Answer to Problem 3CTE

  

Explanation of Solution

Given information:

To draw a large triangle and then make a circle in it.

Calculation:

First of all, we have to consider a triangle $\Delta ABC$ , and have to find the mid points $E,F,G$ of its respective sides $CA,AB,BC$ .

Then we have to draw perpendiculars $BE,CF,AG$ from the vertices $B,C,A$ on the sides $CA,AB,BC$ respectively.

  

The bisecting point $D$ of three perpendicular is the center of the circle. And now we can draw the circle which meet three sides $CA,AB,BC$ exactly at the points $E,F,G$ .And then by adding them

will get the line $EF=\frac{1}{2}(x+y)$ .