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In $△ A B C$ $A (4, 5, 6), B (3, 2, 1), C (5, 4, 3);$ If p,q,r are length of the medians through A,B,C then increasing order of p,q,r is

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p,q,r

q,p,r

r,p,q

r,q,p

answer is C.

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Detailed Solution

$\begin{aligned} a = B C, b = A C, c = A B \end{aligned}$

$\begin{array}{r} P = \frac{1}{2} \sqrt{2 b^{2} + 2 c^{2} - a^{2}}, q = \frac{1}{2} \sqrt{2 a^{2} + 2 c^{2} - b^{2}} \end{array}$

$r = \frac{1}{2} \sqrt{2 b^{2} + 2 a^{2} - c^{2}}$

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