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What are cyclic quadrilaterals and why r they called so and mention formula and also mention the figures that r cyclic quadrilaterals

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by karthik2

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by karthik2

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If all the 4 vertices of a quadrilateral are on a circle, then the quadrilateral is called cyclic. The circle is circum circle.

Formula: s = semipeimeter = 1/2 (AB+BC+CD+DA)

Area of ABCD = √[ (s - AB)(s - BC)(s - CD)(s-D) ]

Sum of opposite angles is 180 deg.

Area is also = 1/2 [ AB BC + CD DA ] Sin ABC

Figures are cyclic quadrilaterals iff Angle ACB = angle ADB

Formula: s = semipeimeter = 1/2 (AB+BC+CD+DA)

Area of ABCD = √[ (s - AB)(s - BC)(s - CD)(s-D) ]

Sum of opposite angles is 180 deg.

Area is also = 1/2 [ AB BC + CD DA ] Sin ABC

Figures are cyclic quadrilaterals iff Angle ACB = angle ADB

The sum of the opposite angles is always equal to 180 degrees.

Area of a cyclic quadrilateral = where a, b, c, d are sides.

Square, Rectangle, isosceles trapezium are perfect examples for cyclic quadrilaterals.