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TS EAMCET · Maths · Straight Lines

If the Circumcenter of the triangle formed by the points \(A(a, 3), B(b, 5)\) and \(C(a, b)\) is \((1,1)\), then out of all the possible coordinates of \(\mathrm{C}\) the sum of the absolute values of the distinct coordinates of \(\mathrm{C}\) is

  1. A 8
  2. B 9
  3. C 12
  4. D 4
Verified Solution

Answer & Solution

Correct Answer

(B) 9

Step-by-step Solution

Detailed explanation

\(\because \mathrm{OP} \perp \mathrm{AC}\) \(\Rightarrow 12=(\mathrm{a}-\mathrm{b})(\mathrm{a}+\mathrm{b}-2)\) ...(i) Putting the value of \(b=-1\) and \(b=3\) in equation (i) we get coordinate of \(\mathrm{C}\) are \((5,3),(-3,3)(5,-1)\) and \((-3,-1)\) Now sum of the absolutes…