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Isosceles Right Triangle in Equilateral Triangle by Inscribed Circles (Dr Geo geometry file)

Two half equilateral triangles (30°-60°-90° triangles) are positioned, with the side of one triangle as the hypotenuse of the next. A circle is inscribed in each triangle. Notice that two lines sloped at 45 degrees form a right isosceles triangle. Do you notice any other geometric coincidences in this diagram? File type drgeo for Dr Geo dynamic geometry software. A coloured png image of this construction is on as Isoscelesinequilateraltriangle.png

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