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)

Circles 3

 

This problem has a nice extension.

If the larger circle has radius R1, the middle sized circle has radius R2 and the smallest circle has radius r show that

formula1

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

Merry Christmas!


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