MathDB

1

Part of 2005 India National Olympiad

Problems(1)

M is the midpoint of the side BC of a triangle ABC

Source: INMO 2005 Problem 1

8/23/2005
Let MM be the midpoint of side BCBC of a triangle ABCABC. Let the median AMAM intersect the incircle of ABCABC at KK and L,KL,K being nearer to AA than LL. If AK=KL=LMAK = KL = LM, prove that the sides of triangle ABCABC are in the ratio 5:10:135 : 10 : 13 in some order.
geometryratiogeometry unsolvedINMO