An angle can be subtended by a line segment or curve. The legs of the subtended angle meet the endpoints of the line segment or curve.

Checking and securing understanding of the parts of a circle

Maths

The angle at the centre of the circle is twice the angle at any point on the circumference

The angle in a semicircle is a right angle

The perpendicular from the centre of a circle to a chord bisects the chord

The tangent at any point on a circle is perpendicular to the radius at that point

The angles in the same segment are equal

The alternate segment theorem

The opposite angles of a cyclic quadrilateral sum to 180°

The tangents from an external point are equal in length

Identifying which circle theorem to use

Problem solving with circle theorems

In the prior unit, pupils applied their understanding of angles to solve increasingly complex problems. In this unit, pupils will use their developed mathematical reasoning skills to derive and use various circle theorems.

In this unit, pupils will use their developed mathematical reasoning skills to derive and use various circle theorems.

Circle theorems

An arc of a circle is part of the circle’s circumference.

The radius is any line segment that joins the centre of a circle to any point on its circumference.

A chord is any line segment joining two points on the circumference of a circle.

The diameter of a circle is any line segment that starts and ends on the circumference of the circle and passes through the centre of the circle.

To bisect means to cut or divide an object into two equal parts.

A tangent of a circle is a line that intersects the circle exactly once.

Two lines are perpendicular if they meet at right angles.

A theorem is a statement that can be proved using known mathematical facts and reasoning.

Two segments are created when dividing a circle into two parts using a chord.

A cyclic quadrilateral is a quadrilateral where all four of its vertices lie on a single circle.

Points A and B are equidistant from a third point C if the distance AC is equal to the distance BC.

Circle theorems

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These lessons will be removed by end of Summer Term 2025.

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