PN is a secant intersecting a circle at points M and N such that PN > PM. A tangent PT
is drawn to the circle touching it at T. If PM = 32 cm and PT = 40 cm, what is the length
(in cm) of the chord MN?
Correct Answer:
@.
Explanation:
According to the tangent-secant theorem, the square of the tangent segment length equals the product of the entire secant segment and its external portion (PT^2 = PM * PN). Substituting the given values, 40^2 = 32 * PN, which means 1600 = 32 * PN, so PN = 50 cm. Since PN is the sum of PM and the chord MN, the length of MN is 50 - 32 = 18 cm.
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