Question

2) PQ is a tangent drawn from a point to a circle with centre O and QOR is a diameter of the
circle such that anglePOQ = 60°. Find angle OPQ.​

Answer 1

Given- PQ is a tangent to a circle with centre O at Q. QOR is a diameter of the given circle so that ∠POQ= 60° . To find ∠OPQ=?

Solution- QOR is a diameter.

∴OQ is a radius through the point of contact Q of the tangent PQ.

∴∠OQP=90° since the radius through the point of contact of a tangent to a circle is perpendicular to the tangent.

∴∠OPQ+ ∠OQP= 60°

(external angles of a triangle=sum of the internal opposite angles )

∴∠OPQ= 30°