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1 week, 3 days ago

# Solve! - Co-ordinate geometry - JEE Main-3

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)

$\frac{60}{13}$

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P Plabita
Answered 1 week, 3 days ago

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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