MathDB

Moldova NMO, 2007, XI Grade, Problem 3

Source: Not very difficult

March 3, 2007

geometry3D geometryanalytic geometrygeometry unsolved

Problem Statement

ABCDA_{1}B_{1}C_{1}D_{1}

is a cube with side length

4a

. Points

E

and

F

are taken on

(AA_{1})

and

(BB_{1})

such that

AE=B_{1}F=a

G

and

H

are midpoints of

(A_{1}B_{1})

and

(C_{1}D_{1})

, respectively. Find the minimum value of the

CP+PQ

, where

P\in[GH]

and

Q\in[EF]