Solving problems using circle theorems - Higher - Circle theorems - Higher - OCR - GCSE Maths Revision - OCR

Solving problems using circle theorems - Higher

Explore updated revision resources for GCSE Maths: Solving problems using circle theorems, with step-by-step slideshows, quizzes, practice exam questions, and more!

Circle can be used to solve more complex problems.

It may not be possible to calculate the missing angle immediately. It may be necessary to calculate another angle first.

Calculate the angles \(a\), \(b\), \(c\) and \(d\).

Using the alternate segment theorem:

angle \(a\) = 65°

Angles in a triangle add up to 180°.

\(b = 180 - 45 - 65 = 70^\circ\)

Opposite angles in a cyclic quadrilateral add up to 180°.

\(d = 180 - 45 = 135^\circ\)

Tangents which meet at the same point are the same length. Angles in a triangle add up to 180°.

\(c = 180 - 65 - 65 = 50^\circ\)