TS EAMCET · Maths · Straight Lines
\(y-x=0\) is the equation of a side of a triangle ABC. The orthocentre and circumcentre of the triangle ABC are respectively \((5,8)\) and \((2,3)\). The reflection of orthocentre with respect to any side of the triangle lies on its circumcircle. Then the radius of the circumcircle of the triangle is
- A 5
- B \(2 \sqrt{5}\)
- C \(\sqrt{10}\)
- D \(2 \sqrt{10}\)
Answer & Solution
Correct Answer
(D) \(2 \sqrt{10}\)
Step-by-step Solution
Detailed explanation
Let H be the orthocentre \((5,8)\) and the side be \(x-y=0\). Reflection of H w.r.t. \(x-y=0\) is \(H' = (8,5)\). The circumcentre is \(O = (2,3)\). Radius \(R = \text{distance}(O, H')\). \(R = \sqrt{(8-2)^2 + (5-3)^2}\) \(R = \sqrt{6^2 + 2^2}\) \(R = \sqrt{36 + 4}\)…
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