Question

# The centre of a circle of radius 13 units is the point (3, 6). P(7, 9) is a point inside the circle. APB is a chord of the circle such that AP = PB. Calculate the length of AB.

Solution

## R.E.F image $$AP = PB \Rightarrow$$ 'P' is mid pt$$\boxed{AB = 2PB}$$$$PB^{2}+OP^{2} = 13^{2}$$ (In $$\Delta OPB)$$$$OP^{2} = \sqrt{(7-3)^{2}+(9-6)^{2}} = \sqrt{4^{2}+3^{2}} = 5$$$$\therefore PB^{2} = \sqrt{13^{2}-5^{2}} = 12$$$$\Rightarrow \boxed{AB = 24\,unit}$$ Mathematics

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