# If the angle of intersection at a point where two circles with radii $5\: cm$ and $12\: cm$ intersects is $90^{\circ}$, then the length (in cm) of their common chord is : Option 1)$\frac{13}{2}$Option 2)$\frac{13}{5}$Option 3)$\frac{120}{13}$Option 4)$\frac{60}{13}$

Length of common chord = $2x$

$\sqrt{s^{2}-x^{2}}+\sqrt{12^{2}-x^{2}}=13$

$x=\frac{12\times 5}{13}$

$2x=\frac{120}{13}$

Option 1)

$\frac{13}{2}$

Option 2)

$\frac{13}{5}$

Option 3)

$\frac{120}{13}$

Option 4)

$\frac{60}{13}$

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