JEE Mains · Maths · STD 11 - 10.1 circle and system of circle
If the angle of intersection at a point where the two circles with radii \(5\, cm\) and \(12\, cm\) intersect is \(90^o\), then the length (in \(cm\)) of their common chord is
- A \(\frac{{13}}{2}\)
- B \(\frac{{120}}{13}\)
- C \(\frac{{13}}{5}\)
- D \(\frac{{60}}{13}\)
Answer & Solution
Correct Answer
(B) \(\frac{{120}}{13}\)
Step-by-step Solution
Detailed explanation
Let length of common chord \(=2x\) \(\sqrt {25 - {x^2}} + \sqrt {144 - {x^2}} = 13\) After solving \(x = \frac{{12 \times 5}}{{13}}\) \(2x = \frac{{120}}{{13}}\)
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