Hayley Steele

2023-02-26

Two congruent circles with centres at (2,3) and (5,6), which intersect at right angles, have radius equal to?

Cailyn Knight

Circles naturally cross at a 90 degree angle.
Given that circles have the same radius, they are congruent.
Then ${r}_{1}={r}_{2}=r$
${C}_{1}{C}_{2}=\sqrt{\left(5-2{\right)}^{2}+\left(6-3{\right)}^{2}}\phantom{\rule{0ex}{0ex}}{C}_{1}{C}_{2}=\sqrt{18}$
By pythagoros theorem
${r}^{2}+{r}^{2}=\left({C}_{1}{C}_{2}{\right)}^{2}\phantom{\rule{0ex}{0ex}}⇒2{r}^{2}=\left(\sqrt{18}{\right)}^{2}\phantom{\rule{0ex}{0ex}}⇒{r}^{2}=9\phantom{\rule{0ex}{0ex}}⇒r=3$

Do you have a similar question?