GCSE Maths Practice: circle-theorems

Question 9 of 10

This multiple-answer question reviews several Circle Theorems simultaneously.

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\( \begin{array}{l}\text{Which statements are true according to Circle Theorems?}\end{array} \)

Select all correct options:

\( \text{Angle at center is twice angle at circumference} \) \( \text{Angle in a semicircle is } 90^\circ \) \( \text{Opposite angles of a cyclic quadrilateral add to } 180^\circ \) \( \text{Tangent crosses the circle} \)

Review each theorem carefully; eliminate any invalid statements.

Key Circle Theorems include: the angle at the center is twice the angle at the circumference; the angle in a semicircle is 90°; opposite angles of a cyclic quadrilateral add to 180°. Understanding these theorems allows students to solve problems with arcs, chords, and tangents, reason about angles, and perform calculations in GCSE geometry. Practising multiple theorems together improves speed, accuracy, and confidence when tackling diagrams with multiple properties.