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(52794)   (Show Source):
You can put this solution on YOUR website! .
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.
------------------------------------------------------------------------------------------------------------------------------------------------------------
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°.
|
|
|
