In a circle with center O, AB is a chord and PQ is a tangent at point T on the circle. The chord AB is extended to meet the tangent PQ at point P. If AB = 9 cm and BP = 16 cm, what is the length of the tangent PT?

Applying the tangent-secant theorem, the square of the tangent length equals the product of the external secant segment and the entire secant length. The entire secant length PA is the sum of PB and AB, which is 16 + 9 = 25 cm. Setting up the equation PT^2 = PB * PA gives PT^2 = 16 * 25 = 400, so PT = 20 cm.

• Thanks
• Wrong explanation