Question

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

Answer 1

Consider this $\Delta$,
PQ = 8 cm

$AO=\sqrt{5^2-4^2}=3$
$\Rightarrow tan\theta =\frac{4}{3}$
Now consider $\Delta POT$,

$\Rightarrow tan\theta =\frac{x}{5}=\frac{4}{3}$
$\Rightarrow x=\frac{20}{3}cm$