AP EAMCET · Maths · Circle
Length of the common chord of two circles of same radius is \(2 \sqrt{17}\). If one of the two circles is \(x^2+y^2+6 x+4 y-12=0\), then acute angle between the two circles is
- A \(\frac{\pi}{2}\)
- B \(\operatorname{Sin}^{-1}\left(\frac{3}{5}\right)\)
- C \(\operatorname{Cos}^{-1}\left(\frac{9}{25}\right)\)
- D \(\operatorname{Tan}^{-1}\left(\frac{9}{17}\right)\)
Answer & Solution
Correct Answer
(C) \(\operatorname{Cos}^{-1}\left(\frac{9}{25}\right)\)
Step-by-step Solution
Detailed explanation
\(r = \sqrt{3^2+2^2-(-12)} = \sqrt{9+4+12} = \sqrt{25} = 5\) \(2\sqrt{17} = 2\sqrt{r^2 - (d/2)^2}\) \(17 = 5^2 - (d/2)^2\) \(17 = 25 - d^2/4\) \(d^2/4 = 8\) \(d^2 = 32\) \(\cos\theta = \frac{r^2+r^2-d^2}{2rr}\) \(\cos\theta = \frac{5^2+5^2-32}{2(5)(5)}\)…
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