Solving problems using circle theorems - Higher
Circle theorems 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.
Example
Calculate the angles \(a\), \(b\), \(c\) and \(d\).
Using the alternate segment theorem:
angle \(a\) = 65掳
Angles in a triangle add up to 180掳.
\(b = 180 - 45 - 65 = 70^\circ\)
Opposite angles in a cyclic quadrilateral add up to 180掳.
\(d = 180 - 45 = 135^\circ\)
Tangents which meet at the same point are the same length. Angles in a triangle add up to 180掳.
\(c = 180 - 65 - 65 = 50^\circ\)