Question

PQ is a tangent drawn from an external point P to a circle with centre O, QOR is the diameter of the circle. If ∠POR = 120°, what is the measure of ∠OPQ?

Answer 1

Given: PQ is the tangent to the circle with centre O. QOR is the diameter.

\[\angle POR = 120^o\]

In\[∆ POQ\]

\[\angle PQO = 90^o\]                                              (tangent at any point of a circle is perpendicular to the radius through the point of contact)

\[\angle OPQ + \angle PQO = \angle POR\]                           (Exterior angle = sum of interior opposite angles)

\[\angle OPQ + 90^o = 120^0\]
\[ \Rightarrow \angle OPQ = 120^o - 90^o = 30^o\]