# A challenging question for Christmas

My favorite two topics are Pythagoras’ Theorem and Circles. This problem combines both, and also has a nice extension which will get the old ‘grey matter’ working again after the break.

The diagram shows three circles all lying along a line which is tangential to all three circles.

- The large circle has a radius of 4.
- The middle sized circle has a radius of 2.
- Show that the radius of the smallest circle is 4(3 - 2√2)

This problem has a nice extension.

If the larger circle has radius R_{1}, the middle sized circle has radius R_{2 }and the smallest circle has radius r show that

This problem featured on Presh Talwalker’s YouTube channel Mind Your Decisions. To watch a solution click here

Merry Christmas!

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