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Q.

$I, I_{1}, I_{2}, I_{3}$ are incentre and excentres of triangle ABC. If $I (0, 0), I_{1} (2, 3), I_{2} (5, 7)$ then distance between orthocentres of $Δ I I_{1} I_{3}$ and $Δ I_{1} I_{2} I_{3}$ is

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a

$\sqrt{74}$

b

25

c

$\sqrt{13}$

d

5

answer is D.

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Detailed Solution

Distance between the $I_{2}$ and $I = \sqrt{5^{2} + 7^{2}} = \sqrt{74}$

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I,I1,I2,I3 are incentre and excentres of triangle ABC. If I(0,0),I1(2,3),I2(5,7) then distance between orthocentres of ΔII1I3 and ΔI1I2I3 is