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Contents
Cyclic Quadrilaterals
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Cyclic Quadrilaterals A quadrilateral with its four vertices lying on the circumference of a circle is called a cyclic quadrilateral.
Property 1 In a cyclic quadrilateral, the opposite angles are supplementary, Proof: Let b = 50 2d = 360
- 100 = 260
d =
260/2 = 30
b +
d =
30 + 50 = 180.
Property
1 can be abbreviated as opp. Ðs
of cyclic quad.
Property 2
If one
side of a cyclic quadrilateral is produced, the exterior angle so formed is
equal to the interior angle.
Proof
b + d =
180°(opp. angles of cyclic quad.)
 x + d =
180°(adj. angles on a str. l)
b + d =
x + d
b = x
angle
ABC = angle CDE
Property 2 can be abbreviated as ext.Ð
of a cyclic quad.
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