Find equation of the Nine Point Circle of Triangle ABC.

Question

In $\Delta ABC , m\angle ABC = 90 .$ Let $S$ be the circumcircle of $ \Delta ABC .$
$ S : x^2+y^2=25 .$ Tangent with negative slope from $(11,-2)$ touches $S$ at $B$.
Find equation of the Nine POint Circle of $\Delta ABC$

I figured out the logic to the problem but I can not understand how to get the co-ordinates of $B$. Thanks

Answer 1

The hint.

Try to explain the following.

Let $B(a,b).$

Hence, we need to solve the following system: $$a^2+b^2=25$$ and $$\frac{b}{a}\cdot\frac{b+2}{a-11}=-1.$$