Similar Triangles Determined by Miquel Circles and the Circumcircle

Let ABC be a triangle and let , , and be points on BC, CA, and AB, respectively. Suppose that the circumcircles of , , and (the Miquel circles) intersect the circumcircle of ABC at points , , and , respectively, where , , and . Let , , and be symmetric to , , and with respect to the midpoints of BC, CA, and AB, respectively. Then and are similar.

THINGS TO TRY

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.