An obtuse triangle and its circumcenter

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  • Thread starter Thread starter chaotixmonjuish
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SUMMARY

The discussion centers on proving that the circumcenter of an obtuse triangle lies outside the triangle itself. The user references a circle with center O and diameter AD, noting that triangle ABC is inscribed within this circle. They mention that according to Proposition III.20, angle BOC is twice the size of angle A, which is crucial for the proof. The user expresses difficulty in creating a synthetic proof despite confirming the concept using Geometer's Sketchpad (GSP).

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  • Understanding of circumcenters in triangle geometry
  • Familiarity with inscribed angles and their properties
  • Knowledge of synthetic proof techniques in geometry
  • Experience with Geometer's Sketchpad (GSP) for geometric visualization
NEXT STEPS
  • Study the properties of circumcenters in obtuse triangles
  • Learn about inscribed angles and their relationships in circles
  • Explore synthetic proof methods in Euclidean geometry
  • Practice using Geometer's Sketchpad (GSP) for geometric constructions
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Students of geometry, mathematics educators, and anyone interested in advanced triangle properties and geometric proofs.

chaotixmonjuish
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I'm having a bit of difficulty proving this, but this is what I have so far:

Let a circle with a center O and a diameter AD. Let triangle ABC be a triangle with all points on the circle and angle A be greater than 90. Because of III. 20, and BOC is 2 times the size of angle A.

This is all I can reason through. I can see that it works on GSP, but I haven't been able to create a synthetic proof.
 
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Could be my English fails me, but I have no idea what you are trying to prove.
 
I'm trying to prove that the circumcenter of an obtuse triangle lies outside of the triangle.
 

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