Question

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

Solution

## Let $$O$$ be the common center of two concentric circles and let $$AB$$ be a chord of larger circle touching the smaller circle at $$P$$ join $$OP$$Since $$OP$$ is the radius of the smaller circle to any chrod of the circle bisects the chord.$$\therefore$$ $$AP =BP$$In right $$\Delta APO$$ we have$$OA^2 = AP^2 + OP^2 \Rightarrow 25 - 9 = AP^2$$$$\Rightarrow AP^2 = 16 \Rightarrow AP = 4$$Now $$AB = 2 , AP = 2 \times 4 = 8 [ \because AP =PB ]$$hence the length of the chord of the larger circle which touches the smaller circle is $$8 cm$$.Maths

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