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Reflective properties of conics, and the Law of Cosines

Here are a couple of new approaches to proving the reflective properties of conics, and the Law of Cosines. The aim is to make the explanations more visual and intuitive than those that are currently presented in textbooks.

• Google Slides of my talk on this topic, presented at MoMath's MOVES 2025 conference.
  
  
• A more detailed write-up of the explanation of the reflective properties of conics.
  
  
• A video on YouTube presenting the more visual and intuitive explanation of the Law of Cosines.

More video explanations

• An intuitive visual proof of the Inscribed Angle Theorem.
  
  
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  The surprising geometry of aiming a soccer ball at a goal.