Since the chords are on opposite sides of the center, the sum of their distances from the center equals 23 cm. Using the Pythagorean theorem on the right triangles formed by the radius, half the chord length, and the distance to the center, we set up the equations r squared equals x squared plus 8 squared and r squared equals (23 minus x) squared plus 15 squared. Equating the two expressions gives x squared plus 64 equals 529 minus 46x plus x squared plus 225, which simplifies to 46x equals 690, so x equals 15. Substituting x back into the first equation gives r squared equals 15 squared plus 8 squared, which equals 225 plus 64 equals 289, meaning the radius is 17 cm.