Intersections 68784

The figure shows the circles k₁(S₁; r1=9 cm) and k₂(S2; r2 = 5 cm). Their intersections determine a common chord t 8 cm long. Calculate the center distance |S₁ S₂| in cm to two decimal places.

Correct answer:

x =  11.06 cm

Step-by-step explanation:

$$\begin{gathered} r_1=9\text{cm} \\ {r}_2=5\text{cm} \\ t=8\text{cm} \\ y=t/2=8/2=4\text{cm} \\ {x}_1=\sqrt{r_1^2-y^2}=\sqrt{9^2-4^2}=\sqrt{65}\text{cm}\doteq 8.0623\text{cm} \\ {x}_2=\sqrt{r_2^2-y^2}=\sqrt{5^2-4^2}=3\text{cm} \\ x=x_1+x_2=8.0623+3=11.06\text{cm} \end{gathered}$$

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