1. ## compass question

So i have a hw problem that gives a picture of a broken dinner plate with a little bit of a rounded circular edge and then a jagged edge, and I am supposed to find the center of the plate with just a compass and straight edge.

2. Originally Posted by igottaquestion
So i have a hw problem that gives a picture of a broken dinner plate with a little bit of a rounded circular edge and then a jagged edge, and I am supposed to find the center of the plate with just a compass and straight edge.
In an unbroken circle,
if you joint the centre to any 2 points on the circumference,
all 3 points then form an isosceles triangle.

An isosceles triangle is formed of 2 identical back-to-back right-angled triangles, which means that if you bisect the base of an isosceles triangle,
then join the base midpoint to the 3rd vertex, you will have formed identical right-angled triangles inside the isosceles triangle.

Going in reverse, if you draw a chord across the round part of the broken plate, then the isosceles triangle base is the line joining the 2 points on the circumference (the chord).
Hence if you bisect this chord and draw the perpendicular bisector, the circle centre lies on this line.
Draw a 2nd chord, bisect it, draw a 2nd perpendicular bisector.
The centre also lies on this line, hence the circle centre is the point of intersection of the perpendicular bisectors of the chords.

3. Hi igottaquestion,
here's an illustration.