# Maths - Circle Theorems

> Source: https://ollybritton.com/notes/a-level/maths/topics/circle-theorems/ · Updated: 2024-08-25 · Tags: maths, circles

##### 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](paste-b221f5669c633d3ddec375463769e15e1e1cf8d2.jpg) What is true about angles created from the same arc (think slice of pie)??
They are equal.

##### ![PHOTO CIRCLE THEOREM ANGLES SEMI CIRCLE](circle-theorem-angle-in-semi-circle.png) 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](circle-theorem-tangent-angle.png) 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](circle-theorem-tangent-equal-length.png) What is always true about the length to the meeting point of two tangents?
It is always equal.

##### ![PHOTO CIRCLE THEOREM ANGLE AT CENTRE](circle-theorem-angle-at-centre.png) 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](circle-theorem-alternate-segment-theorem.png) 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](circle-theorem-cyclic-quadrilateral.png) What's true about opposite angles in a cyclic quadrilateral??
They always add up to $180^\circ$.

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