Circle Theorems.

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Presentation transcript:

Circle Theorems

Angle in a Semicircle There is always a 90º angle opposite the diameter.

Angle at the Centre is Twice the Angle at the Circumference X Y

Opposite Angles in a Cyclic Quadrilateral add up to 180º X Y

Angles in the Same Segment are the Same X

Radius and Tangent meet at 90º

A B C AC=BC Any two tangents from the same point are the same length. The angle between the tangent and the radius drawn to meet it is 90º.

Alternate Segment Theorem X Y There are two pairs of equal angles. One made at the tangent line is equal to the angle in the triangle on the opposite side.

Questions Find angle a and b Find angle a and b Find angle c and d Find angle b