Prove the theorem which states that the angle subtended by a cord is twice at the centre than at the circumference

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Explanation:

Given:

Prove:

Proof:

∠BOA +∠BOC +∠AOC = 360° . . . . . sum of arcs of a circle is 360°

2α +∠BOA = 180°, 2β +∠AOC = 180° . . . . . sum of triangle angles is 180°

∠BOA = 180° -2α, ∠AOC = 180° -2β . . . . solve statement 2 for central angles

(180° -2α) +∠BOC +(180° -2β) = 360° . . . . . substitute into statement 1

∠BOC = 2(α +β) . . . . . add 2α+2β-360° to both sides

∠BOC = 2×∠BAC . . . . . substitute given for α+β; the desired conclusion

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step-by-step explanation: