In a circle with centre O, AD is a diameter and AC is a chord. B is a point on AC, such that OB = 5 cm and ∠OBA = 60°. If ∠DOC = 60°, then what is the length of BC?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 5 cm
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Concept |
Understanding |
Application |
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Angles opposite to the equal sides are equal.
Angle made at semicircle is right angle. |
Given OB = 5 cm ∠OBA = 60° ∠DOC = 60° |
Since OC = OD = Radius ∠OCD = ODC = (180 – 60)/2 = 60 Now ∠BCO = ∠ACO = 90° - ∠OCD = 90° - 60° = 30° In ∆BOC, External ∠OBA = ∠OCB + ∠BOC 60° = 30° + ∠BOC ∠BOC = 30° Since, ∠BOC = ∠OCB = 30° Then, OB = BC Hence, BC = 5 cm. |