Question

Two circles of radii $10$cm and $8$cm intersect and the length of the common chord is $12$ cm, find the distance between their centres.

Answer 1

$\because B{O}_{1}is{\perp }_{r}toAC\therefore AB=\frac{AC}{2}=\frac{12}{2}=6cmin\Delta AB{O}_{1}andAB{O}_{2}byu\sin gpythogorastheoremA{B}^2+B{O_1}^2=A{O_1}^{2}B{O}_1=\sqrt{A{O_1}^2-A{B}^2}=\sqrt{{\left(8\right)}^2-{\left(6\right)}^2}=\sqrt{64-36}=\sqrt{28}unitandB{O}_2=\sqrt{A{O_2}^2-A{B}^2}=\sqrt{{\left(10\right)}^2-{\left(6\right)}^2}=\sqrt{100-36}=\sqrt{64}unitThendis\tan cebetweentheircentresis\left(B{O}_1+B{O}_2\right)=\sqrt{28}+\sqrt{64}$

$2\sqrt{7}+8unit$