More about Pythagorean Triangles

Question

Draw a circle and an arbitrary diameter, creating the base of a triangle. Pick a third point on the circumference to complete the triangle. What is the angle at that third point, and why?

Answer 1

The other approach for this problem is using the fact, that an inscribed angle measure is half of the enclosed arc. The diameter divides the circle into two identical parts. So, the angle would be half of that half of the circle.

Answer 2

Simply draw a radius from that third point to the center of the circle and "split" the original triangle into two new triangles. Look at the interior angles of the two triangles and remember that the sum of interior angles in a planar triangle is 180°.