A Parallelogram and 2 Circles

Geometry Level 4

In Parallelogram ABCD, \(AB=13\), \(BC=11\), and \(AC=20\). Two congruent circles are inscribed in \(\triangle ACD\) and \(\triangle ACB\) as shown in the figure.

The shortest distance between the centers of the two inscribed circles can be expressed in the form \(a\sqrt{b}\). Where \(b\) is a square-free integer. Find the value of \(a+b\).

Found this somewhere.

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 5 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.