# Circles (A_{62}): Sanchez-García triplet circle

### Definition

Consider the tangents from O_{1} to (O_{2}) and O_{2} to (O_{1}) intersecting at H.
Create J in such a way that triangle JO_{1}O_{2} has H as its incenter.
The incircle of this triangle meets the sides JO_{1} and JO_{2} in P and Q respectively.
The circle with diameter PQ is Archimedean circle (A_{62}).
Note that if JO_{1} meets (O_{1}) in K and the circle with diameter CK is Archimedean circle (A_{50a}).
Similarly if JO_{2} meets (O_{1}) in L, and the circle with diameter CL is Archimedean circle (A_{50b}).
[Miguel Ochoa Sanchez (conjecture) and Emmanuel Antonio José García (proof), june 2014]

Source: A. Bogomolny, Shedding Light on the Ball for Eyeballing from Interactive Mathematics Miscellany and Puzzles
http://www.cut-the-knot.org/pythagoras/LightingTheBall.shtml

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