MathDB

2014.8

Part of Swiss NMO - geometry

Problems(1)

concyclic wanted, midpoints of altitudes in acute related

Source: Switzerland - Swiss MO 2014 p8

7/16/2020
In the acute-angled triangle ABCABC, let MM be the midpoint of the atlitude hbh_b through BB and NN be the midpoint of the height hch_c through CC. Further let PP be the intersection of AMAM and hch_c and QQ be the intersection of ANAN and hbh_b. Show that M,N,PM, N, P and QQ lie on a circle.
geometryConcyclicaltitudes