Question

Draw a circle. Can you inscribe an obtuse triangle? If so, tell how many you can draw. If not, explain why not.

No, I cannot draw an obtuse triangle because the greatest angle that can be made inside a circle is a 90° angle.



Yes, I can draw exactly one obtuse triangle.


Yes, I can draw two obtuse triangle.


Yes, I can draw infinitely many obtuse triangle.

Answer 1

Yes, I can draw exactly one obtuse triangle. Every circle has an inscribed triangle with any three given angle measures (summing of course to 180°), and every triangle can be inscribed in some circle (which is called its circumscribed circle or circumcircle). Every triangle has an inscribed circle, called the incircle.

Explanation: