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 = ?

Question

Philoid · Accepted 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