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 :
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 :
Updated On: Jun 23, 2024
- $\frac{60}{13}$
- $\frac{120}{13}$
- $\frac{13}{2}$
- $\frac{13}{5}$
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The Correct Option is B
Solution and Explanation
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} $
$\sqrt{25-x^{2}} + \sqrt{144-x^{2}} = 13$
after solving
$ x = \frac{12\times5}{13} $
$ 2x = \frac{120}{13} $
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