Q5 of 53 Page 158

is a median of ΔABC. If BD = AD, prove that ∠A is a right angle in ΔABC.


In Δ ABC, using Apolloneous Theorem, we know that,


For AD to be the median, we have,


AB2 + AC2 = 2(AD2 + BD2)


As it is given that AD = BD,


⇒ AB2 + AC2 = 4.BD2


Since AD is the median to line BC, we have,



Substituting the value of BD in above equation, we get,


AB2 + AC2 = BC2


So, by the converse of Pythagoras Theorem, we can say that ∠BAC is a right angle.


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