AP EAMCET · Maths · Straight Lines
The orthocentre and the centroid of \(\triangle A B C\) are \((5,8)\) and \(\left(3, \frac{14}{3}\right)\) respectively. The equation of the side \(B C\) is \(x-y=0\). Given that the image of the orthocentre of a triangle with respect to any side lies on the circumcircle of that triangle, then the diameter of the circumcircle of \(\triangle A B C\) is
- A \(\sqrt{10}\)
- B \(2 \sqrt{10}\)
- C \(4 \sqrt{10}\)
- D \(8 \sqrt{10}\)
Answer & Solution
Correct Answer
(C) \(4 \sqrt{10}\)
Step-by-step Solution
Detailed explanation
The centroid on a non-equilateral triangle divides the line joining orthocentre and circumcentre in \(2: 1\), so let the coordinates of circumcentre is \((h, k)\), then…
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