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 = 60°. If ∠DOC = 60°, then what is the length of BC (in cm) ?
Answer & explanation
Correct answer: option 2
\(\angle\)DOC = \({60}^\circ\)
\(\angle\)DOC + \(\angle\)AOC = 180 (Sum of the angles on a straight line is 180)
= 60 + \(\angle\)AOC = 180
= \(\angle\)AOC = 120
In \(\Delta \)AOC,
AO = OC (Radius of the circle)
= \(\angle\)OAC = \(\angle\)OCA = \(\frac{(180\; - \;120)}{2}\) = \({30}^\circ\)
= \(\angle\)OBC = 180 - 60 = 120
= \(\angle\)BOC = 180 - 120 - 30 = 30
\(\angle\)BOC = \(\angle\)OCB = 30
In \(\Delta \)BOC,
OB = BC (Isosceles triangle)
= OB = 7 cm
= BC = 7 cm
Therefore, BC is 7 cm.