List questions from power-of-the-point | MathQA

CGMO 2020: Prove that $X, P, Q, Y$ are concyclic.

Published on 10 Aug 2020 - 15:25

Let $AD\cap (BFC) $ in points $P$ and $Q$ and let $AD\cap (ABE)=M$ then $MP=MQ$.

Published on 12 Aug 2020 - 6:09

Show that all lines XY pass through point H

Published on 11 Oct 2020 - 2:28

Proof of cyclicity using power of a point

Published on 27 Oct 2020 - 17:10

$4$ points in order $A,B,C,D$ lie on a circle with the extension of $AB$ meeting the extension of $DC$ at $E$ and that of $AD$ and $BC$ at $F$.

Published on 01 Nov 2020 - 17:09

To prove $EA = FB$ or that $CQ'$ is radical axis

Published on 23 Feb 2026 - 2:38

Prove that $AM = MF$ where $M$ is the intersection between the perpendicular of circle $ω$ and line $AF$

Published on 06 Nov 2020 - 4:51

Power of a point tangents

Published on 05 Dec 2020 - 19:40

Finding the length of $DE$ given $AB = 4$ and $BE = 5$

Published on 19 Dec 2020 - 4:24

Given tangents from A and C, find minimum length of AC

Published on 01 Feb 2021 - 13:25

Convex quadrilateral geometry and circumradius

Published on 22 Mar 2021 - 10:56