MathDB

2

Part of 2022 China Second Round A1

Problems(1)

Passing through midpoint

Source: 2022 China Second Round A1

12/22/2022
In acute triangle △ABC\triangle ABC, HH is the orthocenter, BDBD,CECE are altitudes. MM is the midpoint of BCBC. PP,QQ are on segment BMBM,DEDE, respectively. RR is on segment PQPQ such that BPEQ=CPDQ=PRQR\frac{BP}{EQ}=\frac{CP}{DQ}=\frac{PR}{QR}. Suppose LL is the orthocenter of △AHR\triangle AHR, then prove: QMQM passes through the midpoint of RLRL.
geometry