Q. 123.7( 3 Votes )

In the given figure, AB is a chord of a circle with centre O and BOC is a diameter. If OD AB such that OD = 6cm then AC = ?


A. 9 cm

B. 12 cm

C. 15 cm

D. 7.5 cm

Answer :

Given: and OD = 6cm


Here OB is radius


Let OB = x cm


In ΔBOD, By Pythagoras theorem


OB2 = BD2 + OD2


x2 = BD2 + 62


x2 = BD2 + 36


BD2 = x2 – 36


Now consider Δ ABC


Here BC = 2x


By Pythagoras theorem


BC2 = AB2 + AC2


(2x)2 = 4(x2 – 36)+ AC2


4x2 = 4x2 –144 + AC2


AC2 = 144


AC = 12 cm


AC = 12 cm

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