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

OB^{2} = BD^{2} + OD^{2}

x^{2} = BD^{2} + 6^{2}

x^{2} = BD^{2} + 36

BD^{2} = x^{2} – 36

Now consider Δ ABC

Here BC = 2x

By Pythagoras theorem

BC^{2} = AB^{2} + AC^{2}

(2x)^{2} = 4(x^{2} – 36)+ AC^{2}

4x^{2} = 4x^{2} –144 + AC^{2}

AC^{2} = 144

AC = 12 cm

∴ AC = 12 cm

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