Common internal tangent of two circles PA is the radius of a circle with center P, and QB is the radius of a circle with center Q, so that AB is a common internal tangent of the two circles, Let M be the midbout of AB and N be the point of line PQ so that line MN is perpendicular to PQ. Z is the point where AB and PQ intersects.  If PA=5, QB=10, and PQ=17. compute PN.
So I tried to compute the problem above and I found the ratio between triangle ZMN:PAN:BQZ is 1:2:4. After finding that I discovered that the distance from both circles is 2, so after some work I found MN to be 2.5 and MZ to be 17/6 but when I used the pythogerom therom to find ZN thus getting a weird answer (8/6). Ultimately my answer for PN was incorrect and I don't know how to solve this problem. Please help me. 

Since $BQ=10$, $AP=5$ and triangles $BQZ$ and $APZ$ are similar, we get $QZ=2PZ$.  Because $PQ=17$, we get $PZ=17/3$ and $QZ=34/3$.  Using the Pythagorean theorem, we get $BZ=16/3$ and $AZ=8/3$, and thus $AB=8$.  Since $MZ=AB/6$, we get $MZ=8/6$ (and not 17/6 as you computed).  Could you do the rest of the computation?
