3) Cyclic quadrilaterals
A cyclic quadrilateral is a quadrilateral drawn inside a circle. Every vertex of the quadrilateral must touch the circumference of the circle.
The second shape is not a cyclic quadrilateral. One vertex does not touch the circumference. The opposite angles in a cyclic quadrilateral add up to 180°.
α + c = 180° and b + d = 180°
Calculate the angles α and b.
The opposite angles in a cyclic quadrilateral add up to 180°.
b = 180° – 140° = 40° and α = 180° – 60° = 120°
Let angle CDE = x and angle EFC = y.
The angle at the centre is twice the angle at the circumference.
Angle COE = 2y and the reflex angle COE = 2x.
Angles around a point add up to 360°.
2x + 2y = 360° so x + y = 180°