Video narration
How many circles can touch all three lines? Think of the lines as three sides of a triangle. Inside is the familiar answer: one circle touching every side-the incircle. But don't stop there. Those three lines also surround three outside regions, and each region holds a circle tangent to all three lines. These are the triangle's excircles. So, how many circles? Four: one incircle inside the triangle, plus three excircles outside. Three non-concurrent lines determine four tangent circles.