In figure,
, where P, Q and R are points on a circle with centre O. Find
.
Solution:
P, Q and R are the points on a circle with centre O where
Construction: S is a point on the major arc PR. Join P and S, R and S to form a cyclic quadrilateral.
(Sum of opposite angles of a cyclic quadrilateral is equal to
)
Also,
(Angle subtended by an arc at the centre is double the angle subtended by it at the circumference of the circle.)
In
, we have
But, we have
(Angles opposite to the equal sides in a triangle are equal.)
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