Why the Three Perpendicular Bisectors Meet: the Circumscribed Circle

Draw the perpendicular bisectors of two sides of a triangle: they cross. Will the third one pass through that same point? Three lines usually make a small triangle — yet the three perpendicular bisectors of a triangle always meet at one point. The full written proof, the circle through the three vertices (the circumscribed circle), where its centre goes as one vertex moves — inside, on a side, outside — the right-angled triangle, and your turn: an isosceles triangle where one perpendicular bisector is found without compass arcs. Timestamps (measured on the final): 0:00 — The third perpendicular bisector 0:42 — Concurrent lines 1:11 — Same distance from both ends 1:34 — Why they meet 2:09 — O is on the third one 2:48 — Where is the centre? 3:28 — The right-angled triangle 3:53 — Your turn 5:03 — Let's remember 🎓 Free interactive lesson: https://commeunjeu.org/cours/ib-myp-2... ▶️ The whole series “Shapes”:    • Shapes   🎵 Music: "Ever Mindful" by Kevin MacLeod (incompetech.com) Licensed under Creative Commons: By Attribution 4.0 http://creativecommons.org/licenses/b...