In ABC, AB = 10, AC = 7, BC = 9 then find the length of the median drawn from point C to side AB


Let CD is the median drawn from C to AB.
Given AB = 10
AD = (1/2)×AB [D is the midpoint of side AB]
AD = 10/2 = 5
Since CD is the median
AC2+BC2 = 2CD2+2AD2 [Apollonius theorem]
72+92 = 2 CD2+2×52
2 CD= 72+92-2×52
2 CD= 80
CD2 = 40
Taking square roots on both sides
CD = 2√10
Hence the length of median drawn from point C to side AB is 2√10 units.

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