Chapter 15.7, Problem 17WE

To determine

To find:

The triangles can be constructed having any three points as vertices.

Answer to Problem 17WE

  $20$

Explanation of Solution

Given:

Seven points lie on the circle

  $A,B,C,D,E,F,G$

Concept used:

First take the points $A,B,C$

  $A\text{and}B$ as two points

  $ABC,ABD,ABE,ABF$

  $A\text{and}C$ as two points

  $ACD,ACE,ACF$

Calculation:

Let Seven points lie on the circle

  $A,B,C,D,E,F,G$

Take only $3$ points

First take the points $A,B,C$

  $A\text{and}B$ as two points

  $ABC,ABD,ABE,ABF$

  $A\text{and}C$ as two points

  $ACD,ACE,ACF$

  $A\text{and}D$ as two points

  $ADE,ADF$

  $A\text{and}E$ as two points

  $AEF$

So, total triangles

  $\begin{array}{l}=4+3+2+1+3+2+1+2+1+1\\ =20\end{array}$