Kenmotu point

Geometry Level 5

Below is triangle \(ABC\) with vertices \(A=(0,0), B=(21,0), C=(5,12).\) The first Kenmotu point for this triangle is \(Q.\) Find the distance \(AQ\) to two decimal places.

Note: The first Kenmotu point is the triangle center constructed by inscribing three identical squares such that each square touches two sides of the triangle and all three squares touch at a single common point.

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