STUDENT TRI-SECTS ANGLE BUT CAN'T UNDERSTAND IT

This is the season for trisecting angles and other such exercises. This is how you do it: Construct an angle, any angle. Bisect it. At a point, any point, on the line of bisection, draw lines to sides of angle and perpendicular to bisector. You have now got a straight angle within the original angle. Using the point as center and length of equal perpendiculars as radius, describe a semi-circle upon the straight angle and within the original angle. Trisect the straight angle by trisecting the semi-circle. The points of trisection of the straight angle will also trisect the original angle.

A History concentrator brought it in last night, says he figured it out last month, has been worrying ever since, doesn't know what's wrong. It appears that it works.