Question

In a circle, a tangent PT is drawn from a point P which touches at point T to the circle and a secant PAB is drawn which intersects the circle at A and B. If PT = 15 cm and AB = 16 cm, then the length of PA is

• A.
  25 cm
• B.
  16 cm
• C.
  15 cm
• D.
  9 cm

Answer 1

The correct option is D

9 cm
Given: PT= 15 cm and AB= 16 cm



$\text{Apply Tangent Secant Theorem}\Rightarrow PA\times PB=P{T}^2\Rightarrow PA\times (PA+16)={15}^2\Rightarrow P{A}^2+16PA-225=0\Rightarrow P{A}^2+25PA-9PA-225=0\Rightarrow (PA-9)(PA+25)=0\Rightarrow PA=9orPA=-25\text{As Length can't be negative.}\Rightarrow PA=9cm$

Hence, the correct answer is option d.