Two chords

Two parallel chords are drawn in a circle with a radius r = 26 cm. One chord has a length of t1 = 48 cm, and the second has a length of t2 = 20 cm, with the center lying between them. Calculate the distance between two chords.

Correct answer:

v₁ =  34 cm
v₂ =  14 cm

Step-by-step explanation:

$$\begin{gathered} r=26\text{cm} \\ {t}_1=48\text{cm} \\ {t}_2=20\text{cm} \\ {x}_1=\sqrt{r^2-(t_1/2{)}^2}=\sqrt{26^2-(48/2{)}^2}=10\text{cm} \\ {x}_2=\sqrt{r^2-(t_2/2{)}^2}=\sqrt{26^2-(20/2{)}^2}=24\text{cm} \\ {v}_1=x_2+x_1=24+10=34\text{cm} \end{gathered}$$

$v_2=|x_2-x_1|=|24-10|=14\text{cm}$

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