question_answer

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:                 [JEE Main Held on 12-4-2019 Morning]

A) \[\frac{60}{13}\]                                

B) \[\frac{120}{13}\]

C) \[\frac{13}{2}\]                                  

D) \[\frac{13}{5}\]

Correct Answer: B

Solution :

          Let length of common chord \[=2x\]\[\sqrt{25-{{x}^{2}}}+\sqrt{144-{{x}^{2}}}=13\]after solving \[x=\frac{12\times 5}{13}\]               \[2x=\frac{120}{13}\]