Cicle Theorems

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Angles Subtended on the Same Arc


Angles formed from two points on the circumference are equal to other angles, in the same arc, formed from those two points.

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Angle in a Semi-Circle


Angles formed by drawing lines from the ends of the diameter of a circle to its circumference form a right angle. So c is a right angle (90 degrees).

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Angle with a Tangent


A tangent to a circle forms a right angle with the circle's radius, at the point of contact of the tangent (a tangent to a circle is a line that touches the circumference at one point only).

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Angle at the Centre


The angle formed at the centre of the circle by lines originating from two points on the circle's circumference is double the angle formed on the circumference of the circle by lines originating from the same points. i.e. a = 2b.

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Alternate Segment Theorem


This diagram shows the alternate segment theorem. In short, the red angles are equal to each other and the green angles are equal to each other.

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Cyclic Quadrilaterals


A cyclic quadrilateral is a four-sided figure in a circle, with each vertex (corner) of the quadrilateral touching the circumference of the circle. The opposite angles of such a quadrilateral add up to 180 degrees.

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thanks very useful

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