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

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Solution

In $Δ O A M$

$(O A)^{2} = (A M)^{2} + (O M)^{2}$

$(5)^{2} - (3)^{2} = (A M)^{2}$

$(A M)^{2} = 16$

$A M = 4 c m$

So, length of chord $A B = 2 A M = 2 (4) = 8 c m$ .

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

In ΔOAM(OA)2=(AM)2+(OM)2(5)2−(3)2=(AM)2(AM)2=16AM=4cmSo, length of chord AB=2AM=2(4)=8cm.

In $Δ O A M$

$(O A)^{2} = (A M)^{2} + (O M)^{2}$

$(5)^{2} - (3)^{2} = (A M)^{2}$

$(A M)^{2} = 16$

$A M = 4 c m$

So, length of chord $A B = 2 A M = 2 (4) = 8 c m$ .