Question

In the given figure, LMN is tangent to the circle with centre O. If $\angle$ PMN = ${60}^{\circ }$, find $\angle$ MOP.

• A. ${30}^{\circ }$
• B. ${60}^{\circ }$
• C. ${90}^{\circ }$
• D. ${120}^{\circ }$

Answer 1

The correct option is D

${120}^{\circ }$

OMN = ${90}^{\circ }$
Radius and tangent are perpendicular at point of contact remaining part of $\angle$OMN is $\angle OMP={90}^{\circ }-{60}^{\circ }={30}^{\circ }$
OP = OM = Radius
Hence, $\angle$OMP = $\angle$OPM = ${30}^{\circ }$

Therefore, $\angle$MOP = ${120}^{\circ }$.