## To calculate the radius of the circle, we can make use of the properties of a circle and the given information.

Let's denote the radius of the circle as 'r'.

We are given two parallel chords of lengths 24cm and 10cm, which lie on opposite sides of the circle, and are 17cm apart.

Now, we can use a property of a circle that states: "If two chords of a circle are parallel, they cut off congruent arcs from the circle."

Since the chords are 17cm apart and the lengths of the chords are given as 24cm and 10cm, the longer chord will cut off an arc of length 24cm, and the shorter chord will cut off an arc of length 10cm.

To find the distance from the center of the circle to each chord, we can use the formula:

Distance from center to chord = 0.5 * sqrt(2 * r^2 - c^2)

where 'r' is the radius of the circle and 'c' is the length of the chord.

For the longer chord (24cm), the distance from the center of the circle to the chord would be:

Distance_1 = 0.5 * sqrt(2 * r^2 - 24^2)

For the shorter chord (10cm), the distance from the center of the circle to the chord would be:

Distance_2 = 0.5 * sqrt(2 * r^2 - 10^2)

Since the chords are parallel and lie on opposite sides of the circle, the sum of the distances from the center of the circle to each chord would be equal to the distance between the chords, which is 17cm:

Distance_1 + Distance_2 = 17

Substituting the calculated values for Distance_1 and Distance_2, we get:

0.5 * sqrt(2 * r^2 - 24^2) + 0.5 * sqrt(2 * r^2 - 10^2) = 17

Simplifying the equation and solving for 'r', we would get the value of the radius of the circle to the nearest whole number.