Two circles of radii $5$ cm and $3$ cm intersect at two points and the distance between their centers is $4$ cm. The length of the common chord is

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Solution

The correct option is A $6$ cm
In the above figure,

PO $= 25 - (4 - x)^{2} = 9 - x^{2}$

$\Rightarrow 9 - x^{2} + 8 x = 9 - x^{2}$

$\Rightarrow x = 0$

$\Rightarrow$ center of the smaller circle lies on the common chord (see the figure)

$\Rightarrow$ The length of common chord =The diameter of smaller circle $= 6 c m$

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Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centres is 4 cm. Find the length of the common chord.

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Two circles of radii 5 cm and 3 cm intersect at two points and the distance between their centers is 4 cm. The length of the common chord is

The correct option is A 6 cmIn the above figure,PO=25−(4−x)2=9−x2⇒9−x2+8x=9−x2⇒x=0⇒center of the smaller circle lies on the common chord (see the figure) ⇒The length of common chord =The diameter of smaller circle =6cm

Two circles of radii $5$ cm and $3$ cm intersect at two points and the distance between their centers is $4$ cm. The length of the common chord is