radius of circle ext. tangent to 3 circles, externally tangent also
Source: Dutch NMO 2008 p4
August 28, 2019
geometrytangent circlesradiusDutch MOexternal tangent
Problem Statement
Three circles , with radii respectively, are externally tangent.
In the area enclosed by these circles, there is a circle which is externally tangent to all three circles.
Find the radius of .[asy]
unitsize(0.4 cm);pair[] O;
real[] r;O[1] = (-12/5,16/5);
r[1] = 1;
O[2] = (0,5);
r[2] = 2;
O[3] = (0,0);
r[3] = 3;
O[4] = (-132/115, 351/115);
r[4] = 6/23;draw(Circle(O[1],r[1]));
draw(Circle(O[2],r[2]));
draw(Circle(O[3],r[3]));
draw(Circle(O[4],r[4]));label("", O[1]);
label("", O[2]);
label("", O[3]);
[/asy]