PQ is a diameter of a circle with centre O. R is a point on the circle such that \(\angle QOR=60^\circ\). What is the measure of \(\angle RPQ\)?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 30°
The angle an arc makes at the centre is twice the angle it makes at any point on the rest of the circle. Arc QR makes \(\angle QOR\) at the centre and \(\angle RPQ\) at P.
\(\displaystyle \angle RPQ=\frac{1}{2}\angle QOR=\frac{1}{2}\times60^\circ=30^\circ\)
The same follows from \(\triangle OPR\): OP \(=\) OR (radii) and its exterior angle \(\angle QOR=60^\circ\) is shared equally by the two base angles.
