**Notes on Java and JavaSketchpad Malfunction:**

The use of Java has become a browser and machine dependent issue.

Readers are advised to use a book marklet that converts JavaSketchpad sketches
on this page (or anywhere else on the internet) to work completely
independently of Java.

You can click on the following link to "fix" the java. Convert JavaSketch

Please give feedback,
whether bug reports or other, to the following email address:
wsp@kcptech.com

The Carom Problem

**Problem:** Given points A and C not on a
line, find the point B on the line so that the sum of the lengths
mBA and mCB is as small as possible.

####

**Solution:** Reflect the point **C** across the line
to give a point **C'**. The line segment **AC'** is the shortest
distance between **A** and **C'**.

**AC'** will meet the line at a point, **X. **
The point **X** will solve the problem.
**Justification.** Consider **B** different from
**X**. The reflection of **CB** across the line gives the segment
**C'B**.

**mBA + m CB = mBA + m C'B > m C'A = mC'X + mXA
= mCX + mXA.**
**EOP.**