MathDB

11.3

Part of 2007 Moldova National Olympiad

Problems(1)

Moldova NMO, 2007, XI Grade, Problem 3

Source: Not very difficult

3/3/2007
ABCDA1B1C1D1ABCDA_{1}B_{1}C_{1}D_{1} is a cube with side length 4a4a. Points EE and FF are taken on (AA1)(AA_{1}) and (BB1)(BB_{1}) such that AE=B1F=aAE=B_{1}F=a. GG and HH are midpoints of (A1B1)(A_{1}B_{1}) and (C1D1)(C_{1}D_{1}), respectively. Find the minimum value of the CP+PQCP+PQ, where P∈[GH]P\in[GH] and Q∈[EF]Q\in[EF].
geometry3D geometryanalytic geometrygeometry unsolved