Determine unknown angles and provide justifications using the following circle properties: the angle in a semicircle is 90°, the angle between a tangent and a radius is 90°, the angle at the center is double that at the circumference, angles in the same segment are equal, the opposite angles of a cyclic quadrilateral add up to 180°, and the alternate segment theorem.

Quick explanation

Determine unknown angles and provide justifications using the following circle properties: the angle in a semicircle is 90°, the angle between a tangent and a radius is 90°, the angle at the center is double that at the circumference, angles in the same segment are equal, the opposite angles of a cyclic quadrilateral add up to 180°, and the alternate segment theorem

• This point belongs to Circle theorems I, especially Circle theorems I outcomes.
• You need to be able to determine unknown angles and provide justifications using the following circle properties: the angle in a semicircle is 90°, the angle between a tangent and a radius is 90°, the angle at the center is double that at the circumference, angles in the same segment are equal, the opposite angles of a cyclic quadrilateral add up to 180°, and the alternate segment theorem.
• The key ideas to know are Calculate, Give, and Explain.
• Use the linked flashcards and practice questions to check recall, then practise applying the idea in an exam-style answer.