Since the chord MN divides the chord PK, by hypothesis, in half, we denote the length of the chord PK by 2 * X cm.Then KE = PE = KP / 2 = X cm.
By the property of intersecting chords, the product 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.
X * X = NE * ME.
X ^ 2 = 3 * 12 = 36.
X = 6 cm.
Then the chord length PK = 2 * X = 2 * 6 = 12 cm.
Answer: The length of the chord PK is 12 cm.
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