B

Step 1: This problem could be solved using the geometric theorem that states: "When two chords intersect inside a circle, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord."[c = 2 and d = 24.]



Step 2: Let the length of one segment of the 14 cm chord be x cm. Then the length of the other segment is (14 - x) cm.

Step 3: x(14 - x) = 2(24)[Application of the Theorem.]

Step 4: 14x - x² = 48[Distributive property.]

Step 5: 14x - x² - 48 = 0

Step 6: - x² + 14x - 48 = 0

Step 7: x² - 14x + 48 = 0[Multiply throughout by - 1.]

Step 8: (x - 8)(x - 6) = 0[Factor.]

Step 9: Therefore, x = 8, 6.

Step 10: When x = 8, 14 - x = 6 and if x = 6, then 14 - x = 8. So, the lengths of the segments of the 14 cm chord are 8 cm and 6 cm.