Q. 1

, , are the medians of ΔABC. If BE = 12, CF = 9 and AB2 + BC2 + AC2 = 600, BC = 10, find AD.

Answer :

From the given info,



As AB2 + BC2 + AC2 = 600


and BC = 10,


AB2 + AC2 = 500 ...... (1)


As AD is median,



BD = 5 ...... (2)


In Δ ABC, using the theorem of Apolloneous, we know that,


For AD to be the median, we have,


AB2 + AC2 = 2(AD2 + BD2)


Substituting values for (1) and (2) in above equation,


500 = 2 (AD2 + 52)


250 = AD2 + 25


AD2 = 225


AD2 = 152


AD = 15


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