Question

AC is a chord of a circle with centre O. the tangents at C to the circle meets extended diameter AB at D. show that BD=BC,if√D=√A.

Answer 1

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Answer 2

BD = BC  if ∠D = ∠A if AC is a chord of a circle with centre O. the tangents at C to the circle meets extended diameter AB at D

Step-by-step explanation:

AB is Diameter

Hence ∠ACB = 90°

∠OCD = 90°   as DC is tangent

∠ACO = ∠ACB - ∠OCB =  90° - ∠OCB

∠DCB = ∠DCO - ∠OCB =  90° - ∠OCB

=> ∠ACO = ∠DCB

   ∠A  = ∠D

Given

=> ΔACO ≈ ΔDCB

=> AC/DC = OC/BC = AO/BD

=>  OC/BC = AO/BD

=> BD/BC = AO/OC

OC = AO = Radius  => AO/OC = 1

=>  BD/BC = 1

=> BD = BC  if ∠D = ∠A

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