For questions 9 at 9:05 minutes in this video, greg literally interprets the diagram, now i know that those circle definitely cut the sides of the triangle in half, but isn’t there a more accurate reason to assume that than comparing the diagram.

Let’s take for example circles P and R

If they meet at one point, then they will have 1 tangent in common

This tangent will be perpendicular to the radius from P as well as the radius from R (the bottom 2)

If that is the case then this perpendicular line is the altitude of the equilateral triangle

As we know that the altitude of an equilateral divides the side into equal halves, we can say that raius of P = radius of R

We can do it similarly for (P and Q) and (Q and R)

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