Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Retracircles

## You may also like

### Baby Circle

### Kissing

### Logosquares

Or search by topic

Age 16 to 18

Challenge Level

The circles centres $O$, $A$, $B$ and $C$ touch one another. Prove that the radii of the circles with centres $A$, $B$ and $C$ are in the ratio $1 : 2 : 3$ and that the triangles $OBC$ and $ABC$ are right angled $3 : 4 : 5$ triangles.

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?

Two perpendicular lines are tangential to two identical circles that touch. What is the largest circle that can be placed in between the two lines and the two circles and how would you construct it?

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.