Question

In fig., PT is a tangent to the circle at T and PAB is a secant to the same circle. If PB = 9cm and AB = 5 cm, find PT.

Answer 1

Given AP and AQ are diameters of circles with centre O and O¹ respectively 

∴ ∠ APB = 90° ---( 1) (Angle in a semidrde is a right angle) 

Similarly, ∠ ABQ =  90° ---(2) 

Adding (1) and (2) 

∠ APB + ∠ ABQ = 90° + 90° 

∠ PBQ = 180° 

Hence, PBQ is a straight line 

∴ P, B and Q are collinear.