AD is a median in triangle ABC. If AB^2+AC^2 = 122 and AD = 6. What will be BC?

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Answer 1 · 2018-01-27T05:35:29

# 10#.

By Apollonius Theorem,

#AB^2+AC^2=2(AD^2+BD^2)#.

But, #BD=1/2*BC#.

#:. AB^2+AC^2=2AD^2+2*(1/2*BC)^2#

#rArr AB^2+AC^2=2AD^2+1/2*BC^2#.

Sub.ing the given values, we get,

#122=2*6^2+1/2*BC^2#,

#:. BC^2=2(122-2*36)=100#.

#rArr BC=10#.