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Question
In the figure, the centre of the circle is O and ∠STP = 40°.
- m (arc SP) = ? By which theorem?
- m ∠SOP = ? Give reason.
Solution
Given: ∠STP = 40°
i. m(arc SP) = 2∠STP
⇒ m(arc SP) = 2 × 40° = 80°
Hence, m(arc SP) is 80° by inscribed angle theorem.
ii. m∠SOP = 2 × m∠STP
= 2 × 40° = 80°
As a result, m∠SOP is 80° since the angle subtended by an arc at the centre of the circle is twice the angle subtended by the arc at any point on the circle.
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