Answer:
C. Angle Bisector Theorem
x = 5
PO = 34
Explanation:
The theorem used is C: Angle bisector theorem
A can be eliminated because there is no midsegment here
B can also be eliminated - no perpendicular bisector
D relates to a median and there is no median here
C is the best choice. You can see in the figure that EO bisects ∠NEP.
Because of this angles ∠NEO and ∠OEP are equal
That makes the triangles congruent since we have one common side and two angles that are equal to each other
Therefore PO = NO
8x - 6 = 6x + 4
8x - 6x = 4 + 6
2x = 10
x = 5
PO = 8(5) - 6 = 40 - 6 = 34