In the adjoining figure, ${A B}^{2} + {A C}^{2} = 122$ and $B C = 10$ . Find the length of the median on side $B C$ .

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Solution

Given, $B C = 10$ and $A B^{2} + A C^{2} = 122$
Since, $B C = 10$ cm , $B Q = \frac{1}{2} B C = 5$ cm
By Apollonius theorem,
$A B^{2} + A C^{2} = 2 (A Q^{2} + B Q^{2})$
$122 = 2 (A Q^{2} + 5^{2})$
$A Q^{2} = 61 - 25$
$A Q = 6$ cm
Length of median = 6 cm

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