TS EAMCET · Maths · Circle
Two circles which touch both the coordinate axes intersect at the points A and B. If \(\mathrm{A}=(1,2)\), then \(\mathrm{AB}=\)
- A 5
- B 13
- C \(2 \sqrt{2}\)
- D \(\sqrt{2}\)
Answer & Solution
Correct Answer
(D) \(\sqrt{2}\)
Step-by-step Solution
Detailed explanation
\( (x-r)^2 + (y-r)^2 = r^2 \) \( (1-r)^2 + (2-r)^2 = r^2 \) \( 1 - 2r + r^2 + 4 - 4r + r^2 = r^2 \) \( r^2 - 6r + 5 = 0 \) \( (r-1)(r-5) = 0 \Rightarrow r_1=1, r_2=5 \) Circle 1: \( (x-1)^2 + (y-1)^2 = 1 \) Circle 2: \( (x-5)^2 + (y-5)^2 = 25 \) Subtracting C1 from C2:…
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