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.

28°

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°