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    Question

    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).
    A 31° Correct Answer Incorrect Answer
    B 28° Correct Answer Incorrect Answer
    C 62° Correct Answer Incorrect Answer
    D 56° Correct Answer Incorrect Answer

    Solution

      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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