Circle centers

What does the diagram below suggest about the relationship between chords in a circle and the center of the circle?
If any three non-collinear points are marked, is it true that a circle can always be drawn through the three points? Try this out with the diagram below;
  • FIRST move the points;
  • try to IMAGINE the circle;
  • click the checkbox to SEE the circle;
Given that the points A (2, 1), B (5, 1) and C (4, 7) lie on the circumference of a circle. Find the coordinates of the centre of the circle, correct to 2-decimal places where necessary! Check your result by inputting the correct equation in the input bar!