GCSE Maths Practice: circle-theorems

Question 3 of 10

This question tests the semicircle theorem, where the angle opposite the diameter is always a right angle.

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\( \begin{array}{l}\text{In a circle, a triangle is drawn with its hypotenuse as the diameter.}\\ \text{What is the angle opposite the diameter?}\end{array} \)

Choose one option:

Angle opposite the diameter = 90°.

In circle geometry, any triangle drawn with the diameter of a circle as one side will have a right angle opposite the diameter. This is called the angle in a semicircle theorem. This property is important for solving geometric proofs, constructing triangles in diagrams, and calculating unknown angles in circles. Practising this theorem ensures students can quickly identify right angles in semicircles, essential for GCSE geometry and reasoning in problems involving tangents, chords, and cyclic quadrilaterals.