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IPMAT Indore 2023 - QA (MCQ) Q31 Explanation
December 31, 2024
Explanation:
(b)
As per the Apollonius theorem for a triangle ABC where D is mid-point of side BC,
AB^2 + AC^2 = 2[BD^2 + 4D^2]
(2x^2) + (3x)^2 = 2[(2x)^2+AD^2]
13x^2/2 − (2x)^2 = AD^2
∴ AD = √5/2 x
Applying Pythagoras theorem in right angled â–³ AMB and â–³ AMC we get
AM^2 = AB^2 – BM^2 …. (1)
AM^2 = AC^2 – MC^2 …. (2)
Now since LHS is equal, RHS should also be equal.
∴ AB^2 – BM^2 = AC^2 – MC^2
⇒ (2x)^2 − k^2 = (3x)^2 − (4x−k)^2
⇒ 4x^2 − k^2 = 9x^2 − 16x^2 − k^2 + 8xk
⇒ 8xk = 11x^2
∴ BM = k = 11/8 x
⇒Thus, BM/AD = 11x/8 / √(5/2 )x = 11/ 4√10 Ans.