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Circle Theorems: Cyclic Quadrilaterals worksheet

Suitable for Year groups: 10, 11
GCSE Tier:
Higher
Targeting grades: 6-7
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Prerequisite knowledge: Calculating missing angles in triangles. Using angle facts such as angles on a straight line and angles around a point. Solving simultaneous equations with two variables.
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Circle Theorems: Cyclic Quadrilaterals worksheet description

This worksheet introduces cyclic quadrilaterals and their angle properties.

The first section helps students identify cyclic quadrilaterals within diagrams, emphasising the recognition of this fundamental shape.

In the second section, students calculate the sizes of missing angles, applying the key rule that opposite angles in a cyclic quadrilateral add up to 180°. This section increases in difficulty starting with straightforward calculations and progressing to using other angle facts such as angles in a triangle or on a straight line. Knowledge of other circle theorems is not required to answer Sections A and B.

Section C incorporates algebraic expressions, as well as other circle theorems. The questions here will be solved using multiple steps and circle theorems such as the angle at the centre is twice the angle at the circumference and more.

Lastly, in Section D learners will form and solve simultaneous equations using cyclic quadrilateral angle properties.

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