Circles have different angle properties described by different circle theorems. Circle theorems are used in geometric proofs and to calculate angles.

Part of

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

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

Calculate the angles EFG and FOG.

Triangle GEF is an isosceles triangle.

Angle FGE = angle EFG

FGE = EFG =

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

Angle EFO = EGO = 90°

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

Angle FOG =

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 congruent because of the SAS rule.

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

One of the angles is equal in size: OCB = OAB

Congruent triangles are identical.

So length CB = AB.