You may also like

Baby Circle

A small circle fits between two touching circles so that all three circles touch each other and have a common tangent? What is the exact radius of the smallest circle?

Logosquares

Ten squares form regular rings either with adjacent or opposite vertices touching. Calculate the inner and outer radii of the rings that surround the squares.

Just Touching

Three semi-circles have a common diameter, each touches the other two and two lie inside the biggest one. What is the radius of the circle that touches all three semi-circles?

Kissing

Age 16 to 18
Challenge Level

The diagram is

 

 

Without loss of generality you can takethe radii of the two identical circles to be 1 unit.

 

Using Pythagoras theorem can you then find the radius of the small circle? Don't worry if you get surds in the answer.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.
Copyright © 1997 - 2023. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project.