Answer:
OM = 24
Step-by-step explanation:
Given that MN and PQ are parallel and PQ intersects the other 2 sides, then it divides those sides proportionally, that is
[tex]\frac{OP}{PM }[/tex] = [tex]\frac{OQ}{QN}[/tex], and substituting values
[tex]\frac{9}{PM}[/tex] = [tex]\frac{12}{32-12}[/tex], that is
[tex]\frac{9}{PM}[/tex] = [tex]\frac{12}{20}[/tex] ( cross- multiply )
12PM = 180 ( divide both sides by 12 )
PM = 15
Thus
OM = OP + PM = 9 + 15 = 24
