PQ is a chord of length 8cm of a circle of radius 5cm and center O. The tangents at P and Q intersect at a point T. Find the length TP.

JoinOTInΔOPTOT2=OP2+PT2⋯(1)OTis perpendicular bisector toPQlet they met atS⟹SP=4cmBy pythagorean theorm⟹SO=3cmBy property associated with altitudes of Right angled triangle⟹ΔOPT≈ΔPSO⟹OSSP=OPPT⟹34=5TP⟹TP=6.66cm