Question

In the figure above, $A$ and $B$ are end points of diameter of a circle with centre at $P$ and $C$ is a point on the circumference of the circle such that $\angle ABC={35}^{\circ }$, the what is the $\angle PCA$?

• A. ${25}^{\circ }$
• B. ${30}^{\circ }$
• C. ${35}^{\circ }$
• D. ${55}^{\circ }$

Answer 1

The correct option is D ${55}^{\circ }$

Given, $\angle ABC={35}^0$

$A,B$ and $C$ are the vertices of the right angled triangle where
$\angle ACB={90}^{\circ }$
$\therefore \angle BAC={90}^{\circ }-{35}^{\circ }={55}^{\circ }=\angle PAC$
Now $\angle PAC={55}^{\circ }$ and $\angle PAC=\angle PCA$
$\therefore \angle PCA={55}^{\circ }$