The chords AB and MN are drawn in the circle, which intersect. In this case, the chord AB is divided by the point

The chords AB and MN are drawn in the circle, which intersect. In this case, the chord AB is divided by the point of intersection into 16cm and 4cm segments, and the chord MN is divided in half. Find the chord MN.

Since the chords AB and MN intersect, to determine the length of the chord MN, we use the intersecting chord property, according to which the product of the segments into which the chords are divided at the intersection of one chord is equal to the product of the segments of the other chord.

MK * NK = AK *   ВK, since MK = NK, then MK ^ 2 = 4 * 16 = 64.

MK = NK = 8 cm, then MN = 2 * 8 = 16 cm.

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