Question

In Fig. AB is a cord of length 16 cm of a circle of radius 10 cm. The tangents at A and B intersect at a point P. Find the length of PA.

Answer 1

OA = 10 cm 

As we know Perpendicular from centre to the chord bisects the chord. 

So AM=MB=8cm 

Using Pythagoras theorem in triangle AOM

\(OM=\sqrt{10^2-8^2}=6\,cm\) 

tan \(\angle AOM=\frac{8}{6}=\frac{4}{3}\)

Now in  ΔOAP

tan \(\angle AOM=\frac{PA}{OA}\)

\(PA=\frac{40}{3}\)