A Concyclic Quartet on a Hyperbola

★ 9/10conic sections analytic geometry Symmetry

Problem

Let $A,B,C,D$ be four points on the hyperbola $xy=k$ . Let $AD$ meet $BC$ at $P$ , let $BD$ meet $AC$ at $Q$ , and let $CD$ meet $AB$ at $R$ . Let $O$ be the origin. Prove that $O,P,Q,R$ lie on one circle.

Answer

Solution

Difficulty	9/10
Topics	conic sections, analytic geometry, Symmetry

Whiteboard

Your sketch is saved only in this browser. To share it, export your drawing as an image (whiteboard menu → Export as → PNG), then upload that image in the comments below.

Discussion

Ask questions, share alternate solutions, and use LaTeX freely.

0 comments

No comments yet.