MathDB

2018.6

Part of Swiss NMO - geometry

Problems(1)

BD = EF wanted, BE// FG incircle related

Source: Switzerland - Swiss ΜΟ 2018 p6

7/14/2020
Let kk be the incircle of the triangle ABCABC with the center of the incircle II. The circle kk touches the sides BC,CABC, CA and ABAB in points D,ED, E and FF. Let GG be the intersection of the straight line AIAI and the circle kk, which lies between AA and II. Assume BEBE and FGFG are parallel. Show that BD=EFBD = EF.
geometryparallelequal segmentsincircle