MathDB

2

Part of 2013 South East Mathematical Olympiad

Problems(1)

China South East Mathematical Olympiad 2013 problem 2

Source:

8/10/2013
△ABC\triangle ABC, AB>ACAB>AC. the incircle II of △ABC\triangle ABC meet BCBC at point DD, ADAD meet II again at EE. EPEP is a tangent of II, and EPEP meet the extension line of BCBC at PP. CF∥PECF\parallel PE, CF∩AD=FCF\cap AD=F. the line BFBF meet II at M,NM,N, point MM is on the line segment BFBF, the line segment PMPM meet II again at QQ. Show that ∠ENP=∠ENQ\angle ENP=\angle ENQ
geometrygeometry unsolved