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A,B,C are points on the circle with centre O. If arc BC =110, m(arc AB) =125, find m(arc ABC) and m(arc AC) |
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Answer» ONG>Answer: 115 Step-by-step explanation: TAKE any POINT P on the circumference of the circle as shown. Join AP and CP.
∵ABC subtends ∠AOC at centre O and ∠APC at any point P on the circumference of the circle. ∴∠AOC=2∠APC ...[∵ Angle subtended by an arc at the centre is twice the angle at the circumference] ∴∠APC= 2 1 ∠AOC[∵AOC=130 ∘ ] ⟹ 2 1 ×130 ∘ =65 ∘ .
∵ ABCP is a cycle QUADRILATERAL, ⟹∠APC+∠ABC=180 ∘ ...[∵ sum of opposite angles of a cyclic quadrilateral is 180 ∘ ] ⟹65 ∘ +∠ABC=180 ∘
∴∠ABC=180 ∘ −65 ∘ =115 ∘ .
Hence, option B is correct. Answered By
Divyanshu |
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