### Intercept theorem in sage

Hi,

I'm working on Grobner bases and Buchberger algorithm and begginning in Sage. I would like to find a way to prove that if we have $B, C, D$ three points, then the point $C$ is in the circle of diameter $BD$ if and only if the triangle $BCD$ is an ~~$C-shaped ~~$C$-shaped right-angled ~~triangle$.~~triangle.

I'm thinking about using the Intercept theorem but I would like to prove it using Sage.

Thank you