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Cyclic Quadrilateral, vertices, circle, supplementary angles
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Cyclic Quadrilateral
A quadrilateral is called a cyclic quadrilateral if its all vertices lie on a circle.
The sums of either pair of opposite angles of a cyclic quadrilateral are supplementary.
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Example: In Fig , if DBC = 80 and BAC = 30. Find BCD.
SOLUTION: Consider the chord CD. We find that CBD and CAD are angles in the same segment of the circle.
80 = CAD
CAD = 80
    BAD = BAC + CAD
BAD = 30 + 80 = 110
Since ABCD is a cyclic quadrilateral. Therefore,
BAD + BCD = 180
110 + BCD = 180
BCD = 70
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