SOLUTION: PA and PB are two tangents drawn from P to a circle with centre 'O'. C is a point on the major arc AB. Angle ACB=80. Find angle APB.

Question 986677: PA and PB are two tangents drawn from P to a circle with centre 'O'. C is a point on the major arc AB. Angle ACB=80. Find angle APB.
Answer by ikleyn(52797) (Show Source): You can put this solution on YOUR website!
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PA and PB are two tangents drawn from P to a circle with centre 'O'. C is a point on the major arc AB. Angle ACB=80. Find angle APB.
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Since the angle ACB is 80�, the measure of the minor arc AB it leans is 2*80� = 160�. Hence, the central angle AOB is of 160�.

Now consider a quadrilateral PAOB. Three of its angles are of 90�, 90� and 160�. (Two angles are of 90� because the radius drawn to the tangent point
is perpendicular to the tangent straight line).

Since the sum of interior angles of a quadrilateral is 360�, the missed angle is (360� - (90� + 90� + 160�)) = 20�. It is exactly the angle APB.

Answer. The measure of the angle APB is 20�.

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