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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?

    Module 2 Day 8 Challenge Part 4
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    • The Blade DancerT
      The Blade Dancer M0★ M1★ M2★ M3★ M4 M5
      last edited by debbie

      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?

      The Blade Dancer
      League of Legends, Valorant: Harlem Charades (#NA1)
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      • N
        nastya MOD M0 M1 M2 M3 M4 M5
        last edited by debbie

        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. 🙂

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