AB is a diameter of a circle with centre O. A tangent is drawn at point A. C is a point on the circle such that BC produced meets the tangent at P. If ∠APC = 62°, then find the measure of the minor arc AC.
Answer & explanation
Correct answer: option 3
We know that,
The radius/diameter of a circle is always perpendicular to the tangent line.
Sum of all three angles of a triangle = 180°
AB = diameter
∠APC = 62º
∠APC = 62º = ∠APB
∠BAP = 90° (diameter perpendicular to tangent)
In Δ APB, ∠APB + ∠BAP + ∠PBA = 180°
= ∠PBA = 180° - (90° + 62°)
= ∠PBA = 28°