Question

How to trisect 90 degree angle

Answer 1

Let AOB be a right angle.

Choose any radius r of the compass and draw a circle of radius r with center O.

This circle will meet the line segment OB at a point P.

Now draw a circle with radius r and center P.

This second circle will meet the first circle at a point Q.

Notice that the triangle OPQ is an equilateral triangle and this each angle is a 60 degree angle.

This means that the angle QOA is a 30 degree angle.