As shown in the figure below, O and Q are the centers of equal intersecting circles at A and B so that OA is tangent to circle Q at A. If S is the area of the triangle OAC and S₁ is the area of the square ACDE, prove that S₁ = 4S
 

See solution below

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Geometric Art of Problem 1428: Sketching, Typography, iPad Apps

See solution below

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Animation of the Conformal Mapping or Transformation of Problem 1428

Conformal Mapping

A conformal mapping or conformal transformation is a continuous mapping preserving the form of infinitesimal figures. This conformal map produces a realistic view of the original image or map. This the conformal transformation of problem1428.

See also: Typography and poster of problem 1426.