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Too many to work with (Posted on 2019-03-21) Difficulty: 4 of 5
Let ABC be a triangle with incircle k. Let D, E and F be the points of tangency of k with AB, BC and CA. Let G be the intersection of DF and BC and H be the intersection of DE and AC (G, H, E and F are on the same side of AB). Let M be the midpoint of FH and N be the midpoint of EG.

If the area of ABMN is 100 and the area of CMN is 4, find the area of EFGH.

Can you generalize this>

No Solution Yet Submitted by Danish Ahmed Khan    
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re: GSP solution Comment 2 of 2 |
(In reply to GSP solution by Jer)

A bit of playing around with the construction leads me to believe the generalization to be:

if ABMN/CMN=x then EFGH/CMN=4sqrt(x)

  Posted by Jer on 2019-03-22 22:35:49
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