A circle O is inscribed in a square ABCD. As shown in the figure below, a circle O_{1} with radius r_{1}
is tangent to the arc BD of center A and
tangent to BC and CD. A circle O_{2}
with radius r_{2} is tangent to circle O and tangent to AB and AD. Prove that r_{1} = 2r_{2}.

### Geometric Art of Problem 1427: Sketching, Typography, iPad Apps

### Animation of the Conformal Mapping or Transformation of Problem 1427

### 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
problem1427

See also:
Typography and poster of problem 1426.