MathGoldMedalist
HomeToolkitProblemsCompetitionsAbout
Sign InRegister
HomeToolkitProblemsCompetitionsAbout
  1. Home
  2. ›
  3. Toolkit
  4. ›
  5. Ptolemy's Theorem

Toolkit 59

Ptolemy's Theorem

Cyclic quadrilateral ABCD with diagonals

A quadrilateral ABCDABCDABCD is cyclic if and only if:

AB⋅CD+AD⋅BC=AC⋅BDAB\cdot CD+AD\cdot BC=AC\cdot BDAB⋅CD+AD⋅BC=AC⋅BD

Related Problems

Core

  • AMC 12A 2024 (Problem 19)
  • AMC 12B 2025 (Problem 25)
← Back to Toolkit
HomeToolkitProblemsCompetitionsAbout

Stay Connected

Sign up for updates and new content.

© 2026 MathGoldMedalist. All rights reserved.