Two parallel chords of a circle with diameter 13 cm are, 5 cm and 12 cm in length. If both the chords lie either side to centre, find the distance between the chords.

Sure, here is the step by step solution:

Step 1: Draw a circle with a diameter of 13 cm. Draw two parallel chords, one 5 cm long and the other 12 cm long, on either side of the center.

Step 2: Draw radii to the endpoints of the chords. This will create two right-angled triangles.

Step 3: The radius of the circle is half the diameter, so it is 13/2 = 6.5 cm.

Step 4: In the right-angled triangle with the 5 cm chord, the hypotenuse is the radius (6.5 cm) and one side is half the chord length (5/2 = 2.5 cm). We can use the Pythagorean theorem to find the other side, which is the distance from the center of the circle to the chord. This distance is sqrt(6.5^2 - 2.5^2) = sqrt(42.25 - 6.25) = sqrt(36) = 6 cm.

Step 5: Similarly, in the right-angled triangle with the 12 cm chord, the hypotenuse is the radius (6.5 cm) and one side is half the chord length (12/2 = 6 cm). The distance from the center of the circle to this chord is sqrt(6.5^2 - 6^2) = sqrt(42.25 - 36) = sqrt(6.25) = 2.5 cm.

Step 6: The distance between the chords is the sum of the distances from the center to each chord, which is 6 cm + 2.5 cm = 8.5 cm.