Izliektā \(7\)-stūrī \(ABCDEFG\) punkti \(A_{1}, B_{1}, C_{1}, D_{1}, E_{1}, F_{1}, G_{1}\) ir attiecīgi malu \(DE,\ EF,\ FG,\ GA,\ AB,\ BC,\ CD\) viduspunkti. Dots, ka \(AA_{1} \perp DE,\ BB_{1} \perp EF,\ CC_{1} \perp FG,\ DD_{1} \perp GA,\ EE_{1} \perp AB\) un \(FF_{1} \perp BC\). Pierādīt, ka \(GG_{1} \perp CD\).