Q9 of 53 Page 158

In ΔABC, m∠A = 90. is a median. If AD = 6, AB = 10, then AC =


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


For AD to be the median, we have,


AB2 + AC2 = 2(AD2 + BD2)


⇒ BC2 = 2 (36 + BD2)


⇒ 4BD2 = 72 + 2BD2


⇒ 2BD2 = 72


⇒ BD2 = 36


⇒ BD = 6


So, BC = 12 as BC = 2BD


By Pythagoras Theorem in ΔABC,


AC2 = BC2 – AB2


⇒ AC2 = 144 – 100


⇒ AC = 2√11


∴ Option (d) is correct.

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