Question

in triangle ABC m is any point on BC . prove AM2 +BC2=AC2+ BM2. 'answer fast'​

Answer 1

IF IT IS AC^2 THEN THE ANSWER IS

FROM TRIANGLE ABC
BC = 2BM

FROM TRIANGLE ABC

BY PYTHAGORAS THEOREM

AC^2 = AB^2+BC^2
I.E AB^2 = BC^2-AC^2 ----(1)

FROM TRIANGLE ABM

AM^2 = AB^2+BM^2 (BY PYTHAGORAS THEOREM)
I.E AB^2 = BM^2-AM^2 ------(2)

FROM (1) & (2)

BC^2-AC^2 = BM^2-AM^2
BC^2-BM^2+AM^2 = AC^2
(2BM)^2-BM^2+AM^2 = AC^2 [BC = 2BM]
4BM^2-BM^2+AM^2 = AC^2
3BM^2+AM^2 = AC^2

AC^2 = AM^2+3BM^2

HENCE PROVED