Segment Length from Parallel Chords in a Circle
Geometry · 28th PMO Qualifying Stage
Points $T, S, P, M$, and $O$ lie on a circle in clockwise order such that $TS$ is parallel to $PO$ and $TP$ is parallel to $MO$. Let lines $TS$ and $PM$ intersect at point $N$. If $PN = 8$, $PM = 12$, and $MO = 30$, what is the length of segment $TP$?
A15
B18
C20
D28