In a circle with center O, AD is a diameter and AC is a chord. Point B is on AC such that OB = 7 cm and ∠OBA = 60°. If ∠DOC = 60°, then what is the length of BC?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 7 cm.
Now, according to the question
∠DOC = 60°
∠DOC + ∠AOC = 180° (Sum of angles on a straight line add up to 180°)
⇒ 60° + ∠AOC = 180°
⇒ ∠AOC = 120°
In △AOC
⇒ ∠OAC = ∠OCA [In a triangle, opposite angles of two equal sides are always equal]
⇒ (180° - 120°)/2 = 60°/2 = 30°
⇒ ∠OBC = 180° - 60° = 120°
⇒ ∠BOC = (180° - 120° - 30°)= 30°
⇒ ∠BOC = ∠OCB = 30°
In △BOC
OB = BC (Isosceles triangle)
⇒ OB = 7 cm
⇒ BC = 7 cm