### Three Points on a Parabola

Let three points A, B, C lie on a parabola with axis OO'. Let AA', BB', CC' be parallel to the axis. Form intersections

P = AB ^ CC', Q = AC ^ BB' R = BC ^ AA'. |

Let the tangents to the parabola at A and B meet at M_{C}, those at A and C meet at M_{B}, and the tangents at B and C meet at M_{A}.

What if applet does not run? |

Prove that

- M
_{A}lies on PQ, M_{B}on PR, and M_{C}on QR. - PQ is parallel the tangent at A, PR at B, and QR at C.

|Activities| |Contact| |Front page| |Contents| |Geometry|

Copyright © 1996-2018 Alexander Bogomolny