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TS EAMCET · Maths · Straight Lines

Let \(A B C\) be a triangle and \(A=(1,2)\). If \(x-3 y-5=0\) and \(x+5 y-9=0\) are the perpendicular bisectors of the sides \(A B\) and \(B C\) respectively, then the length of the side \(A C\) is

  1. A \(\sqrt{34}\)
  2. B \(2 \sqrt{26}\)
  3. C \(2 \sqrt{10}\)
  4. D \(4 \sqrt{2}\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(4 \sqrt{2}\)

Step-by-step Solution

Detailed explanation

\( \begin{aligned} & O P: x-3 y-5=0 \\ & O Q: x+5 y-9=0 \\ & \therefore \quad O\left(\frac{13}{2}, \frac{1}{2}\right) \end{aligned} \) Since \(P\) is mid point of \(A B\). Hence \(P\left(\frac{1+x_1}{2}, \frac{2+y_1}{2}\right)\) \(\because \quad P\) lies on \(O P\) and…