MathDB

6

Part of 2015 Bosnia Herzegovina Team Selection Test

Problems(1)

Incircle geometry

Source: Bosnia and Herzegovina TST 2015 day 2 problem 3

5/18/2015
Let DD, EE and FF be points in which incircle of triangle ABCABC touches sides BCBC, CACA and ABAB, respectively, and let II be a center of that circle.Furthermore, let PP be a foot of perpendicular from point II to line ADAD, and let MM be midpoint of DEDE. If {N}=PM∩AC\{N\}=PM\cap{AC}, prove that DN∥EFDN \parallel EF
geometryincircleincenterperpendicular bisectorparallel