document.write( "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. \n" ); document.write( "
Algebra.Com's Answer #607720 by ikleyn(52798)\"\" \"About 
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\n" ); document.write( "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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\n" ); document.write( "\n" ); document.write( "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°. \r
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\n" ); document.write( "\n" ); document.write( "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 \r
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\n" ); document.write( "\n" ); document.write( "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. \r
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\n" ); document.write( "\n" ); document.write( "Answer.  The measure of the angle  APB  is  20°. \r
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