Question

Two circles touch each other externally at P. AB is a common tangent to the circles touching them at A and B. The value of $\angle APB$ is

• A. ${30}^o$
• B. ${45}^o$
• C. ${60}^o$
• D. ${90}^o$

Answer 1

The correct option is D ${90}^o$

Let $PQ$ be the common tangent through P, where Q is the point that meets $AB$
Now, $QA=QP$ (Tangents to the circle from the same point)
$QP=QB$ (Tangents to the circle from the same point)
Thus, $QA=QP=QB$
Thus, Points $A,B,P$ lie on the circle with centre Q and $AB$ as the diameter.
Thus, $\angle APB={90}^{\circ }$ (Angle in a semi-circle)