Cross-Ratios

Explanations 5

• The cross ratio is a number that is assigned to any set of four collinear points in a projective plane. In this post, we will be working in the real projective plane, also denot…

  By Tae Hyung Kim

• This is part 1 of the cross ratio series. The others are: Part 2 Angle-chasing is one of the most important technique in Olympiad geometry. However, it may not always work, and …

  By Navi Nahc, Ray Li

• This is part 2 of the cross ratio series. The only way to improve math is by examples and lots of practice, so let me continue further with more lemmas and problems. We continue…

  By Navi Nahc

• Let's start with the definition of the ratio. Definition: If A,B,CA,B,CA,B,C are three points on a line, not all equal, then we define their ratio to be (A,B;C)=ACBC,(A,B;C) = \…

  By Zarathustra Elessar Brady

• The Cross Ratio Given four collinear points AAA, BBB, XXX, YYY we define their cross ratio to be (A,B;X,Y)=XAXB:YAYB.(A,B;X,Y) = \frac{XA}{XB} : \frac{YA}{YB}.(A,B;X,Y)=XBXA​:YB…

  By Evan Chen, Expii Team