Question

Ab is the diameter and ac is a chord with centre o such that bac=30

Answer 1

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Answer 2

Step-by-step explanation:

Construction : Join OC, BC

In ΔAOC

OA = OC (radii of same circle)

ACO = OAC = 30

AOC = 180 - (30 + 30) = 120

AOC + BOC = (linear pair)

BOC = 180 - 120 = 60

OCB = 90 - 30 = 60

BCD = 90 -60 = 30

In ΔOCD

ODC = 180 - (60 + 90)

= 30

InΔBCD

BCD = BDC = 30

BD = BC (sides opposite to equal angles)

Hence proved