Question 986677
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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 &nbsp;<B>ACB</B>&nbsp; is &nbsp;80°, the measure of the minor arc &nbsp;<B>AB</B>&nbsp; it leans is 2*80° = 160°. &nbsp;Hence, &nbsp;the central angle &nbsp;<B>AOB</B>&nbsp; is of &nbsp;160°.  


Now consider a quadrilateral &nbsp;<B>PAOB</B>. &nbsp;Three of its angles are of &nbsp;90°, &nbsp;90° &nbsp;and &nbsp;160°. &nbsp;(Two angles are of 90° &nbsp;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 &nbsp;360°, &nbsp;the missed angle is &nbsp;(360° - (90° + 90° + 160°)) = 20°. &nbsp;It is exactly the angle &nbsp;<B>APB</B>. 


<B>Answer</B>. &nbsp;The measure of the angle &nbsp;<B>APB</B>&nbsp; is &nbsp;20°.