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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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