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Geometry puzzle (23) |  |
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Calculate the radius of the small red circle in figure below.
A nice application of the theorem of Pythagoras and the ABC rule (solving Ax2+Bx+C=0)
For clarity the picture is enlarged and lines are added.
Look at ΔABC and apply the Pythagoras theorem:
Look at ΔMNP (NP = d) :
Look at ΔAQN:
Next fill in the values for R and d , simplify:
We notice a veiled quadratic equation, just substitute x2 = r.
Application of the ABC rule:
