/sci/ - Science & Math

This is actually pretty easy but most posters are justifiably too lazy to waste their time doing the boring calculations to get the answer.
You have A1(10, 10), B1(11, 19), C1(15, 18) and A2(23, 10), B2(20, 19), C2(26, 17). Those give you P1(10.5, 14.5), Q1(12.5, 14), P2(21.5, 14.5), and Q2(24.5, 13.5), because of ((x1+x2)/2, (y1+y2)/2).
To get the equation of p1, the perpendicular bisector of A1 and B1 going through P1, you just have to do f(x)=-1/(slope of A1, B1)*x + some bullshit based on the location of P1. That gives you
p1: y = -1/9 * x + 141/9
q1: y = -5/8 * x + 349/16
p2: y = 1/3 * x + 22/3
q2: y = -3/7 * x + 24
Now you have to solve p1 = q1 and p2 = q2 to get O1 and O2.
O1: (885/74, 1061/74)
O2: (175/8, 117/8)
Now you can just calculate the distance between A1 and O1 to get r1 and so on:
r1 = 4.75987 (rounded)
r2 = 4.75986 (rounded)
So now we know that the circle on the left is bigger.