XAB and XCD are two secants to a circle. If XA = 18 cm, AB = 22 cm and XC = 24 cm, then find the value of XD (in cm).
30
The secant-tangent theorem states that the square of the length of the secant segment (XA) minus the product of the lengths of the two segments formed by the secant (AB and XD) is equal to the square of the length of the tangent (XC).
By applying the formula for secants:
(XA)(AB) = (XC)(XD)
Substituting the given values: 18 * 22 = 24 * XD
396 = 24 * XD
Solving for XD gives: XD = 396 / 24 = 30 cm.
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