GCSE Maths Practice: circle-theorems

Question 4 of 10

This question tests the circle theorem that the angle at the center is twice the angle at the circumference.

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\( \begin{array}{l}\text{What is the ratio of the angle at the center to the angle at the circumference subtended by the same arc?}\end{array} \)

Choose one option:

Angle at center = 2 × angle at circumference.

For any circle, the angle subtended at the center by an arc is always twice the angle subtended at the circumference by the same arc. This 2:1 ratio is a fundamental property for solving problems involving angles, arcs, and chords. Understanding this relationship allows students to calculate missing angles, apply theorems to cyclic quadrilaterals, and reason geometrically in diagrams, which is essential for GCSE exams.