Question

In the given figure, if the angle between two chords $AB$ and $AC$ is ${65}^o$, then the angle between two tangents which are draw at $B$ and $C$ is _______

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

Answer 1

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

reffer image

$\angle BOC=2\angle BAC=2\left(65\right)$

$\angle BOC={130}^{\circ }$

in quadrilateral $BOCP-\angle BOC+\angle OCP+\angle CPB+\angle PBO={360}^{\circ }$

${130}^{\circ }+{90}^{\circ }+{90}^{\circ }+\angle CPB$

$\angle CPB={50}^{\circ }$