Chord AB of a circle of radius 10 cm is at a distance 8 cm from the centre O. If tangents drawn at A and B intersect at P., then the length of the tangent AP (in cm) is:

The distance from center O to chord AB is 8 cm. Using the radius OA = 10 cm, half of AB = sqrt(10² - 8²) = sqrt(36) = 6 cm. The distance OP = 8 + 6 = 14 cm (tangent intersection lies on line through center perpendicular to chord). Using Pythagorean theorem in right triangle OAP: AP = sqrt(OP² - OA²) = sqrt(196 - 100) = sqrt(96) = 7.5 cm.