### Proposition

The figure below shows
a right triangle ABC with the circles C_{1}, C_{2}, and C_{3} with diameters AB,
BC, and AC, respectively. C_{1} and C_{2} meet at D and DAE and DCF are
isosceles right triangles. C_{3} meets EF at G and G_{1}. EH is tangent to C_{1}
and FJ is tangent to C_{2}. Circle with center E and radius EH meets the
circle with center F and radius FJ at K and L. If MN is the common external
tangent to C_{1} and C_{2}, prove that GL = MN.

See solution below

## Sketch of Problem 1401 using iPad Apps

See solution below

### Animation of the Conformal Mapping of Problem 1401

### 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 mapping of
problem1401.

### Geometric Art
using Mobile Apps

Geometric art is a form of art based on the use and application of geometric figures. A geometric figure is any set or combination of points, lines, surfaces and solids. A mobile app or mobile application software is a computer program designed to run on smartphones and tablet computers.