Circles

In the circle with a radius 7.5 cm are constructed two parallel chord whose lengths are 9 cm and 12 cm. Calculate the distance of these chords (if there are two possible solutions write both).

Correct result:

x =  10.5 cm
y =  1.5 cm

Solution:

$r^2 = 7.5^2 = x_1^2 + (9/2)^2 \ \\ r^2 = 7.5^2 = x_2^2 + (12/2)^2 \ \\ x_1 = 6 \ cm \ \\ x_2 = 4.5 \ cm \ \\ \ \\ x = x_1+x_2 = 10.5 \ \text{cm}$
$y = |x_1-x_2| = 1.5 \ \text{cm}$

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