Question

In triangle $ABC$; angle $ABC={90}^{\circ }$ and $P$ is a point on $AC$ such that $\angle PBC=\angle PCB$.
Hence: $PA=PB$.

• A. True
• B. False

Answer 1

The correct option is A True

Given: $\angle PBC=\angle PCB=x$
Given: $\angle ABC=90$
$\angle ABC=\angle ABP+\angle PBC$
$90=\angle ABP+x$
$\angle ABP=90-x$ (I)
Now, in $△ABC$,
$\angle ABC+\angle BCA+\angle CAB=180$ (Sum of angles of triangle)
$90+x+\angle CAB=180$
$\angle CAB=90-x$ (II)
From I and II,
$\angle CABor\angle PAB=\angle ABP$
$PA=PB$