Going around incircles | Colin

“Did you know,” asked a student at third-hand1, “that the in-circle of a 3-4-5 triangle has a radius of 1?”

That’s the kind of thing I’d normally just fire up GeoGebra to check, but I was in the middle of a podcast! The best I could do was check to see if it violated anything I could think of, and I blurted out: it doesn’t violate the equal tangents theorem (if two tangents to the same circle meet at a point, the tangents are equal.)

That’s because the in-circle fits snugly into the right angle. If its radius is 1, the tangents on the ‘3’ side are of length 1 and 2, and those on the ‘4’…

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