Circle Theorems

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circle theorems

Inscribed Angle Theorem

Angles in the same segment standing on the same chord are always the same.

Angles in the same segment standing on the same chord are always the same

A line drawn from the centre of a circle to the mid-point of a chord is perpendicular to the chord.

A line drawn from the centre of a circle to the mid-point of a chord is perpendicular to the chord

Circle Theorems: Intersecting Chords Theorem; If $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ are the co-ordinates of the end of the diameter of a circle, then $(x - x_{1}) (x - x_{2}) + (y - y_{1}) (y - y_{2}) = 0$

Circle theorems
Circle theorems - examples: Practice Questions; Textbook Exercise
Right angle in a semi-circle
Angles at circumference\centre
Angles in the same segment
Cyclic quadrilaterals
Alternate segment theorem
Radius and tangent proof: Practice Questions; Textbook Exercise; (Care of corbettmaths.com)

Circle Theorems: Exam Questions; Circle Theorems; Solutions; (Care of www.mathsgenie.co.uk)

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