Why do these two triangles have the same centroid?

Draw any triangle ABC. Construct three similar triangles on its sides: pick any shape you want. The new vertices form a triangle PQR. Here's the strange part: PQR and ABC always share the same centroid. Every shape. Every time. Same exact point. Inspired by Tristan Needham's "Visual Complex Analysis" 🎵 Music: Maarten Schellekens — Last Voyage #math #geometry #mathematics #visualmath #mathbeauty #elegantmath #proof #centroid #triangle #stem #science #curiosity #learning #mathart