I don't get Prof. Loh's criteria for seeing if a shape is cyclic. What does x angle only having 0 to add to itself mean?

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    I don't get Prof. Loh's criteria for seeing if a shape is cyclic. What does x angle only having 0 to add to itself mean?

  • MOD

    Hi @The-Rogue-Blade!

    We assumed that there exist four points that have equal angles as shown on picture below, and we want to prove that these four points lie on the one circle by contradiction.

    M2D8C4-2.jpg

    We know that inscribed angles that subtend the same arc on the circle are equal. So we are drawing an additional line and get one more green angle that equal previous two:

    M2D8C4.jpg

    So now we have a triangle with interior and exterior angles that are equal. Hence, those two points are the same ones. 🙂