Question

In the shown diagram, if the angle between two chords AB and AC is ${65}^0$, then the angle between two tangents which are drawn at B and C is

• A. ${50}^0$
• B. ${30}^0$
• C. ${60}^0$
• D. ${40}^0$

Answer 1

The correct option is A ${50}^0$


$\angle OBP=\angle OCP={90}^0$ [ Radius is always perpendicular to the tangent of the circle]
$\angle BOC=2\times \angle BAC=2\times {65}^0={130}^0$

In quadrilateral BOCP,
$\angle BOC+\angle OCP+\angle CPB+\angle PBO={360}^0$ [ Sum Angle property of Quadrilateral]
$130+90+\angle CPB+90=360$
$\angle CPB={50}^0$
Hence, a is the correct option.