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

## Question

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.

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

Find the centre and radius of the circle orthogonal to the three circles

\begin{align*} x^2+y^2-12x-8y+34 &= 0,\\ x^2+y^2-6x-12y+32 &= 0,\\ x^2+y^2-10x-6y+30 &= 0. \end{align*}