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. (i.e.∠ ABC).
Minor arc AC will create angle CBA ∠APC = 62º = ∠APB ∠BAP = 90° (diameter perpendicular to tangent) In Δ APB, ∠APB + ∠BAP + ∠PBA = 180° ⇒ ∠PBA = 180° - (90° + 62°) ⇒ ∠PBA = 28° ∴ The measure of minor arc AC =28°
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