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>
The area sought is 80.
Rather than make the areas exactly as given, I found if ABMN/CMN=25 then EFGH/CMN=20.
I've tried solving this, but I don't know where to even begin.
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Posted by Jer
on 2019-03-22 14:22:29 |
GSP solution
