Chords AB and CD meet at point K. Find the length of chord AB if CK = 4dm, DK = 15dm, AK: KB = 3: 5.

According to the condition AK / KB = 3/5, then AK = 3 * KB / 5.

By the property of intersecting chords, the product of the lengths of the segments formed at the intersection of one chord is equal to the product of the lengths of the segments of the other chord.

AK * BK = CK * DK.

3 * (KB / 5) * KB = 4 * 15.

3 * KB ^ 2 = 5 * 4 * 15 = 300.

KB ^ 2 = 300/3 = 100.

KB = 10 dm.

Then AK = 3 * 10/5 = 6 cm.

Chord length AB = AK + KB = 6 + 10 = 16 dm.

Answer: The length of the chord AB is 16 cm.