Two tangents AP and AQ are drawn to a circle with centre O from an external point A, where P and Q are points on the circle. If \(\angle PAQ=80^\circ\), what is the measure of \(\angle AOP\)?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 50°
A tangent is perpendicular to the radius at the point of contact, and OA bisects the angle between the two tangents.
\(\angle OAP=\frac{1}{2}\times80^\circ=40^\circ\)
\(\angle OPA=90^\circ\)
In \(\triangle OPA\): \(\angle AOP=180^\circ-90^\circ-40^\circ=50^\circ\)
