alternative angle bisecting technique

several people (mainly Derek Ball) devised an interesting way of constructing an angle bisector in a meeting led by Steph Prestage and Pat Perks (then of Birmingham University)

draw two arcs from the meet point (the intersection of the two lines)

draw the cross diagonals of the resulting isosceles trapezium (or trapezoid)

join this crossover point to the start point

this same device (drawing two arcs) can be adapted to 'drop a perpendicular' to a line from a given point






Pat and Steph stress a view that it is helpful to use full circles rather than just arcs when constructing loci - to aid understanding

however, this can use (and needs) a lot of space...

thanks to Ed Southall