Question

Find the value of PA in the figure given below.

Answer 1

We know that, if PT is a tangent and PAB is a secant to a circle from an extenal point then, $P{T}^2=PA\times PB$.
$\Rightarrow 6^2=PA\times (PA+5)$
$36=(PA{)}^2+5PA)$
Let
PA be x
So,
$36=x^2+5x$
$x^2+5x-36=0$
$(x+9)(x-4)$
x= -9,4
So, x=4cm { as the value of PA can not be negative }
$PA=4cm$

$PA=4cm$