Review question

# What can we say if two circles cut at right angles? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R7925

## Suggestion

Derive a condition for the two circles

\begin{align*} x^2+y^2+2g_1x+2f_1y+c_1 &= 0,\\ x^2+y^2+2g_2x+2f_2y+c_2 &= 0, \end{align*}

to cut orthogonally.

‘Orthogonally’ means ‘at right angles’.

Could we draw a helpful diagram? If we assume two circles cut orthogonally, can we deduce a relationship between their radii and the distance apart of their centres?

Hence, or otherwise, show that in general there is just one circle orthogonal to three given circles.

If such a circle exists, what equations can we write down? When do these equations have a unique solution?