Let ABCD be a parallelogram, with M the midpoint of DA, and diagonal AC of length 36. Let G be the intersection of MB and AC and draw in diagonal DB. What is the length of AG?

Question

anonymous · Answer

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phi · Answer

try to prove triangle AGM is similar to triangle CGM

phi · Answer

once you do,  you see the smaller triangle's sides are exactly 1/2  the bigger triangle's sides

using x= AG,  the length of the corresponding side GC is 2x
together the segments add to 36
we find 3x=36  and x=12