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AP EAMCET · Maths · Circle

\(\mathrm{ABC}\) is a triangle and the radical centre of the circles with \(\mathrm{AB}, \mathrm{BC}, \mathrm{CA}\) as the diameters is \((-6,5)\). Now if \(A=(3,2), B=(2,1)\) then \(C=\)

  1. A \((1,1)\)
  2. B \((1,2)\)
  3. C \((2,3)\)
  4. D \((1,-2)\)
Verified Solution

Answer & Solution

Correct Answer

(D) \((1,-2)\)

Step-by-step Solution

Detailed explanation

\(R(-6,5)\) is the orthocenter of \(\triangle ABC\). Altitude from \(C(x,y)\) to \(AB\) passes through \(R\). \(m_{AB} = \frac{1-2}{2-3} = 1\). Slope of altitude from \(C\) is \(-1\). \(y-5 = -1(x-(-6)) \Rightarrow y-5 = -x-6 \Rightarrow x+y=-1\). Altitude from \(A(3,2)\) to…