Maths - Circle Theorems


What is always true about two radii and a chord in a circle?


They always make an isoceles triangle.

What is always true about the perpendicular bisector of a chord in a circle?


It always passes through the centre of the circle.

PHOTO CIRCLE THEOREM ANGLES SUBTENDED SAME ARC What is true about angles created from the same arc (think slice of pie)?


They are equal.

PHOTO CIRCLE THEOREM ANGLES SEMI CIRCLE What is true about angle C, the angles formed by drawing lines from the ends of a diameter to the circumference?


It is always $90^\circ$.

PHOTO CIRCLE THEOREM TANGENT ANGLE What is true about the angle that a tangent makes with the circumference of a circle?


It is always $90^\circ$.

PHOTO CIRCLE THEOREM TANGENT EQUAL LENGTH What is always true about the length to the meeting point of two tangents?

It is always equal.

PHOTO CIRCLE THEOREM ANGLE AT CENTRE What is always true about the angle at the centre in relation to the angle at the diameter?


The angle at the centre is twice the one at the circumference.

PHOTO CIRCLE THEOREM ALTERNATE SEGMENT THEOREM What’s always true about the angle either side of the triangle?


It’s always equal to the angle opposite.

PHOTO CIRCLE THEOREM CYCLIC QUADRILATERAL What’s true about opposite angles in a cyclic quadrilateral?


They always add up to $180^\circ$.




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