MathDB

3.2

Part of Geometry Mathley 2011-12

Problems(1)

Geometry Mathley 3.2 fixed point

Source:

6/7/2020
Given a triangle ABCABC, a line δ\delta and a constant kk, distinct from 00 and 1,M1,M a variable point on the line δ\delta. Points E,FE, F are on MB,MCMB,MC respectively such that ME‾MB‾=MF‾MC‾=k\frac{\overline{ME}}{\overline{MB}} = \frac{\overline{MF}}{\overline{MC}} = k. Points P,QP,Q are on AB,ACAB,AC such that PE,QFPE, QF are perpendicular to δ\delta. Prove that the line through MM perpendicular to PQPQ has a fixed point.
Nguyễn Minh Hà
fixedFixed pointequal ratiogeometry