What is a half angle?

Answer 1

A half angle is just what it sound like; it's half the measure of an angle. If you have an angle of 30 degrees, the half angle is 15 degrees. Simple and easy. Where it comes in handy is in construction of something like, say, an isosceles triangle inside a circle. If you have the two equal equal angles, you can find the third angle. Then you can construct it by drawing a chord across the circle through its diameter, then using the half angle to draw in one side. Repeating the process on the other side of the diameter will give you the other side of the triangle. By drawing in a chord connecting the points where the other two chords (drawn off the half angles on either side of the diameter) intersect the circle, you'll have completed the construction of the isosceles triangle.