SS2 Second Term Mathematics Lesson Note – Circle Theorem

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WEEK 6

TOPIC: CIRCLE THEOREM

• The angle which an arc subtends at the centre is twice the angle it subtends at the circumference.
• Angles in the same segment of a circle are equal.
• Angle in a semi-circle.
• Tangent to a circle.

PROOF OF (i) The angle which an arc subtends at the centre is twice the angle it subtends at the circumference.

The angle which an arc (or a chord) of a circle subtends at the centre of the circle is twice the angle which it subtends at any point on the remaining part of the circumference.

Note: An arc of a circle is any connected part of the circle’s circumference.

A chord which is not a diameter divides the circle into two arcs- a major and a minor arc.

Given: An arc AB of a circle with ‘O’ and a point ‘P’ on the circumference.

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