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

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

Two lines are perpendicular if they meet at right angles.

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

Problem solving with circle theorems

Maths

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.

Circle theorems

The length of chord MN is {{}} cm (2 d.p.).

$$u = 7k + 4$$.
$$v = 9k$$.
$$u$$° = {{}}°.

The image shows a circle, a tangent to the circle and a number of chords and radii within the circle.
$$b : c : d = 5 : 7 : 6$$.
$$e$$° = {{}}°.

The image shows a circle, a tangent to the circle and a number of chords and radii within the circle.
$$b : c : d = 5 : 7 : 6$$.
$$g : h = 14 : 9$$.
$$h$$° = {{}}°.

The diagram shows a circle with a tangent and three line segments that form a triangle inside the triangle. 
$$c$$° = {{}}°.

Points A and B are points where two separate tangents intersect the circle.
$$c$$° = {{}}°.

Points A and B are points where two separate tangents intersect the circle.
Find the size of angle $$d$$°.

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