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

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Solution

OMN = OMQ = $90^{\circ}$
Radius and tangent are perpendicular to each other at the point of contact. (1 mark)

Therefore, $∠$ OMP = $90 - 60 = 30^{\circ}$
OP = OM = Radius
Hence, $∠$ OMP = $∠$ OPM = $30^{\circ}$

Therefore, $∠$ MOP = $120^{\circ}$ . (1 mark)

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