Casey's theorem
2020 is the bicentenary of the birth of the Irish geometer, John Casey (1820-1891). This applet illustrates Casey's theorem which tells us about the tangents to four non-intersecting circles that are each tangent to another circle. Here we see four circles, blue, green, orange & red (B, G, O & R). Six common (exterior) tangents are shown, two pink, two purple and two brown. Multiply the three pairs of lengths (of the same colour). Casey's theorem tells us that the pink product plus the purple product equals the brown product.
Explore Casey's theorem by moving the B, G, O & R anchor points on the large circle (which has unit radius). The lengths of the tangents and their products are shown, along with the sum of the pink and purple products. You can also change the radius of each of the four circles (by moving their centres).
The coding ensures that circles are constrained so that they do not overlap; for this reason it is recommended that adjustments are made in the order B, G, O & R.