In a circle with centre O, AD is a diameter and AC is a chord. Point B is on AC such that OB = 7 cm and ∠OBA = 60º.If ∠ DOC = 60º, then what is the length ob BC (in cm)?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 7
∠DOC = 60°
∠DOC + ∠AOC = 180° (Sum of the angles on a straight line is 180°)
⇒ 60° + ∠AOC = 180°
⇒ ∠AOC = 120°
In ΔAOC,
AO = OC (Radius of the circle)
⇒ ∠OAC = ∠OCA = (180° – 120°)/2 = 30°
⇒ ∠OBC = 180° – 60° = 120°
⇒ ∠ BOC = (180° – 120° – 30°) = 30°
∠BOC = ∠OCB = 30°
In ΔBOC,
OB = BC
⇒ OB = 7 cm
⇒ BC = 7 cm