Chords AB and CD intersect to point K, and chord AB is divided by point K into segments equal to 10 cm

Chords AB and CD intersect to point K, and chord AB is divided by point K into segments equal to 10 cm and 6 cm. Into which segments does point K divide chord CD if CD is more than AB by 3 cm.

To solve the problem, we will use the property of intersecting chords, which is expressed in the proportion:
CK * KD = AK * KB.
You will need to calculate the length of the chords.
In our case: AB = 16 cm and CD = 19 cm;
Next, you need to make a quadratic equation and find its roots.
The roots will be 4 and 15, both positive and satisfying the solution of the problem.
4 and 15, are the lengths of the segments up to currents K.
ANSWER: CK = 4 cm KD = 15 cm.