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.