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Q.

The distance between the circumcenter and the orthocenter of the triangle whose vertices are (0, 0), (6, 8), and  (-4,3) is L . Then the value of 25L is

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answer is 5.

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Detailed Solution

Given vertices of triangle are O(0,0), 8(6,8), and C(-4,3).Slope of OB=86=43Slope of OC=−34∴ ∠BOC=π2∆OBC is right-angled at O.Circumcenter = Midpoint of hypotenuse BC=1,112Orthocenter = Vertex O(0, 0)Required distance =1+1214=552 units
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The distance between the circumcenter and the orthocenter of the triangle whose vertices are (0, 0), (6, 8), and  (-4,3) is L . Then the value of 25L is