# Geometry Problem 1431: Triangle, Circumcircle, Parallel Chord, Apollonius, LLC, Congruent Angles

The figure below shows a triangle ABC with the circumcircle of center O so that a chord DE is parallel to AC. A circle O1 is tangent to the arc AD and tangent to DE and AB. A circle O2 is tangent to the arc CE and tangent to DE and BC. Prove that the angles ABO1 and CBO2 are congruent.

## Typography and Sketching of Problem 1431 using iPad Apps

### 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 problem1431.

### 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.