Question

If the angle of intersection at a point where the two circles with radii 5 cm and 12 cm intersect is $90^{\circ}$, then the length (in cm) of their common chord is :

• A. $\frac{60}{13}$
• B. $\frac{120}{13}$
• C. $\frac{13}{2}$
• D. $\frac{13}{5}$

Answer 1

Answer: (B)

$\frac{120}{13}$

Answer 2

Let length of common chord = $2x$
$\sqrt{25-x^{2}} + \sqrt{144-x^{2}} = 13$
after solving
$x = \frac{12\times5}{13}$
$2x = \frac{120}{13}$