Tangents - Higher - Circle theorems - Higher - AQA - GCSE Maths Revision - AQA

Tangents - Higher

There are two circle theorems involving .

1. The angle between a tangent and a is 90°.

2. Tangents which meet at the same point are equal in length.

Calculate the angles EFG and FOG.

Triangle GEF is an triangle.

Angle FGE = angle EFG

Angle FGE = angle EFG = \(\frac{180 - 20}{2} = 80^\circ\)

The angle between the tangent and the radius is 90°.

Angle EFO = angle EGO = 90°

The shape FOGE is a . The angles in a quadrilateral add up to 360°.

Angle FOG = \(360^\circ - 90^\circ - 90^\circ - 20^\circ = 160^\circ\)

The angle between the tangent and the radius is 90°.

Angle BCO = angle BAO = 90°

AO and OC are both radii of the circle.

Length AO = Length OC

Draw the line OB. It creates two triangles OCB and OAB. These share the length OB.

Triangles OCB and OAB are because of the RHS rule.

Two of the sides are the same length: OB = OB and OC = OA

One of the angles in each triangle is a right angle: OCB = OAB

Congruent triangles are identical.

So length CB = AB.