Question

If $2$ intersecting circles have a common chord of length $16cm$ and if the radii of $2$ circles are $10cm,17cm$, find the distance between their centres.

Answer 1

$AD=10cm$

$BD=\frac{16}{2}=8cm$

$AB=\sqrt{{10}^2-8^2}$

$=\sqrt{100-64}$

$=\sqrt{36}$

$=6cm$

$CD=17cm$

$BD=\frac{16}{2}=8cm$

$BC=\sqrt{{17}^2-8^2}$

$=\sqrt{289-64}$

$=\sqrt{225}$

$=15cm$

Now,

$AC=AB+BC$

$=6+15$

$=21cm$