Geometry: Angle at the Centre

 Circle: Angle at the Centre The angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the remaining part of the circle.
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Example: In the fig. below, P, R, and S are three points on a circle such that the angles subtended by the chords PS and PR at the centre O are 90 and 120, respectively. Determine SPR.
Solution: Given,
SOP = 90 and POR = 120
Therefore,
 SOR = 360 - (SOP + POR)= 360 - (90 + 120)= 150

Now,
2SPR = SOR
SPR = 1/2SOR
SPR = 1/2 x 150 = 75.

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