Question

State true or false:

The sides $AB$ and $AC$ of a triangle $ABC$ are produced; and the bisectors of the external angles at $B$ and $C$ meet at $P$. Now if $AB>AC$, then $PC>PB$

If true enter 1 else 0

Answer 1

here, $AB>AC$

As we know, $A$ greater angle of a triangle is opposite a greater side.

So, $\angle ACB>\angle ABC$

and external angle will be smaller.

So, $\angle BCF<\angle CBE$

$\frac{1}{2}\angle BCF<\frac{1}{2}\angle CBE$

$\angle BCP<\angle CBP$

As $A$ is greater angle of a triangle is opposite a greater side.

So, $PC>PB$