From a point P outside a circle, PAB is a secant and PT is a tangent to the circle, where A, B and T are points on the circle. If PT = 5 cm, PA = 4 cm and AB = x cm, then x is equal to:

By the tangent-secant theorem, the square of the tangent length PT equals the product of the secant's external segment PA and the entire secant length PAB. Setting up the equation gives 5 squared equals 4 times (4 plus x). This simplifies to 25 equals 16 plus 4x, meaning 4x equals 9. Therefore, x equals 2.25 cm.

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