Shape and Space 6
3 marks · NormalExplain, with reasons, why the points A, B, C, and D in a circle are called concyclic points. Give a geometrical property relating their angles.
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A, B, C, and D are concyclic if they lie on the same circle. Opposite angles in a cyclic quadrilateral add up to 180°.
Must show: definition of concyclic, opposite angles sum to 180°
Common mistakes: Confusing cyclic and regular quadrilaterals
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Marking points
B1 · 1 mark · States that concyclic points lie on a circle.
M1 · 1 mark · Gives the cyclic quadrilateral property: opposite angles add up to 180°.
A1 · 1 mark · Correctly connects the definition to the angle property.
Worked solution
Points are concyclic if they lie on one circle. In a cyclic quadrilateral, the sum of each pair of opposite angles is 180°. This follows from the fact that each pair of angles subtends the same arc.