Two parallel chords

In a circle 70 cm in diameter, two parallel chords are drawn so that the circle's center lies between the chords. Calculate the distance of these chords if one is 42 cm long and the second is 56 cm long.

Final Answer:

v₁ =  49 cm
v₂ =  7 cm

Step-by-step explanation:

$$\begin{gathered} d=70\text{cm} \\ r=d/2=70/2=35\text{cm} \\ {t}_1=42\text{cm} \\ {t}_2=56\text{cm} \\ {x}_1=\sqrt{r^2-(t_1/2{)}^2}=\sqrt{35^2-(42/2{)}^2}=28\text{cm} \\ {x}_2=\sqrt{r^2-(t_2/2{)}^2}=\sqrt{35^2-(56/2{)}^2}=21\text{cm} \\ {v}_1=x_2+x_1=21+28=49\text{cm} \end{gathered}$$

$v_2=|x_2-x_1|=|21-28|=7\text{cm}$

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