Question

For any side of the excentral triangle of triangle ABC, vertices of triangle ABC follows which property?

• A. All vertices lies on same side
• B. Two lies on one side and one lie on other side
• C. One lies on the side of excentral triangle and two vertices lie on either sides of this side
• D. One lies on the side of excentral triangle and two vertices lie on other two sides

Answer 1

The correct option is D One lies on the side of excentral triangle and two vertices lie on other two sides

$I_1{I}_2{I}_3$ is excentral triangle of triangle ABC.

Now,

A is any vertice, it lies on side $I_1{I}_2$ and other two vertices lie on sides $I_1{I}_3$ and $I_2{I}_3$.

Hence, One lies on the side of excentral trianle and two vertices lie on other two sides.