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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 $$ \Delta OPB) $$
$$ OP^{2} = \sqrt{(7-3)^{2}+(9-6)^{2}} = \sqrt{4^{2}+3^{2}} = 5 $$
$$ \therefore PB^{2} = \sqrt{13^{2}-5^{2}} = 12 $$
$$ \Rightarrow \boxed{AB = 24\,unit} $$ 

1115235_528836_ans_9adc2650388647fe8aba2d7fb3c93260.jpg

Mathematics

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