Circle Important Theorems

               Circle Theorem 

Theorem 1 - The perpendicular bisectors of two chords of a circle intersect at its centre. 

Theorem 2- The perpendicular from the centre of a circle to a chord bisects the chord.

Theorem 3- If two arcs of a circle are congruent then the corresponding chords are equal. 

Theorem 4 - The line joining the centre to the mid point of a chord is perpendicular to the chord. 

Theorem 5 - Equal chords of a circle are equidistant from the corresponding centre. 

Theorem 6 -chords which are equidistant from the corresponding centres are equal. 

Theorem 7 - The angle in a semi circle is a right angle. 

Theorem 8 - There is one and only one circle passing through three non collinear points. 

Theorem 9 - An infinite number of circles can be drawn to pass through a single point. 

Theorem 10 - An infinite number of circles can be drawn to pass through two given points. 

Theorem 11 - A unique circle can be drawn to pass through three given non collinear points. 

Theorem 12 - Angle in the same segment of the circle are equal. 

Theorem 13 - The angle subtended by an arc of a circle at the centre is double the angle subtended by it at any point on the circumference of circle. 

Theorem 14- Equal chords of congruent circles are equidistant from the corresponding centres. 

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