MathDB

Movements on skew lines

Source: Czech and Slovak Olympiad 1964, National Round, Problem 2

June 22, 2024

3D geometryfixed lineskew line

Problem Statement

Consider skew lines

PP'

QQ'

and points

X

Y

lying on them, respectively. Initially, we have

X=P

Y=Q

. Both points

X

Y

start moving simultaneously along the rays

PP'

QQ'

with the speeds

c_1

c_2

, respectively. Show that midpoint

Z

of segment

XY

always lies on a fixed ray

RR'

, where

R

is midpoint of

PQ