In a circle of radius 26 cm there are two parallel chords, of lengths 48 cm and 20 cm…

Step 1. The first chord. Half of it is $24\ \text{cm}$. Its distance from the centre is $\sqrt{26^2 - 24^2} = \sqrt{100} = 10\ \text{cm}$.

Step 2. The second chord. Half of it is $10\ \text{cm}$. Its distance is $\sqrt{26^2 - 10^2} = \sqrt{576} = 24\ \text{cm}$.

Step 3. Opposite sides. The perpendicular from the centre is the same line for both chords, so the distance between the chords is $10 + 24 = 34\ \text{cm}$.

Step 4. The same side. The distance is $24 - 10 = 14\ \text{cm}$.