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°
Angles in a triangle add up to 180°.
\(b = 180 - 45 - 65 = 70^\circ\)
Opposite angles in a cyclic quadrilateral add up to 180°.
\(d = 180 - 45 = 135^\circ\)
A straight line that just touches a point on a curve. A tangent to a circle is perpendicular to the radius which meets the tangent. which meet at the same point are the same length. Angles in a triangle add up to 180°.
\(c = 180 - 65 - 65 = 50^\circ\)