ΔABC is inscribed in a circle with centre O. AO is produced to meet the circle at K and AD⊥ BC. If ∠B = 80° and ∠C = 64°, then the measure of ∠DAK is:
Show answer & explanation
Correct answer: A
Explanation
Correct Answer is option 1 i.e. 16°
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Concept |
Understanding |
Application |
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Angle subtended by a chord at centre is double the angle subtended by same chord at circumference of the circle. |
Given AD ⊥ BC, ∠B = 80° and ∠C = 64°
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Join O to B and join O to C where point O is circum-centre of the triangle. ⇒ ∠BOA = 2∠BCA = 2 × 64° = 128° In ΔBOA ⇒ OB = OA (radius of the circle) ⇒ ∠ABO = ∠OAB ⇒ ∠ABO + ∠OAB + ∠BOA = 180° ⇒ 2∠OAB = 180° – 128° = 52° ⇒ ∠OAB = 26° In ΔABD ⇒ ∠ABD + ∠BDO + ∠DAB = 180° ⇒ ∠DAB = 180° – 90° – 80° = 10° ⇒ ∠DAK = ∠BAO – ∠BAD = 26° – 10° = 16° |
