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Question

Two  concentric are of radii $$5 cm $$ and $$3cm $$ . Find the length of the chord of the larger circle which touches the smaller circle.


Solution

Radius of big circle, 
$$OA = OB = 5cm $$
Radius of small circle, $$OP = 3 cm $$
Angle between radius and tangent is $$90^{\circ}$$
$$\therefore \angle OPA = \angle OPB = 90^{\circ}$$
($$\because$$ Chord AB is tangent to small circle )
Now , in $$\perp \bigtriangleup  OPA, \angle OPA = 90^{\circ}$$
$$OP^{2} + AP^{2} = OA^{2}$$
$$(3) ^{2} + AP^{2} = (5) ^{2}$$
$$9 + AP^{2}= 25$$
$$\therefore AP^{2}= 25-9$$
$$AP^{2} = 16$$
$$\therefore AP = 4 cm $$
Similarly , in $$\perp  \bigtriangleup OPB , PB = 4 cm $$
$$\therefore $$ Length of chord , $$AB = AP + PB = 4 + 4 $$
$$\therefore $$ chord , $$AB = 8 cm $$
1832725_1867296_ans_f2da19a3c777415ead8b5bc92ae0b9c8.png

Mathematics

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