Question

In a circle, PM and QN intersect at a point O. If PM = 15 cm, find the length of OM.

• A. 10 cm
• B. 7.5 cm
• C. 5 cm
• D. 6 cm

Answer 1

Answer:

C. 5 cm

Based on the standard geometry problem (where $PM$ and $QN$ are medians of a triangle intersecting at the centroid $O$):

The point of intersection of the medians of a triangle is the centroid, which divides each median in a $2:1$ ratio from the vertex to the midpoint of the opposite side.

• Here, $PM$ is a median, and point $O$ is the centroid.

• This means the ratio of $PO \colon OM = 2 \colon 1$.

• Therefore, segment $OM$ is $\frac{1}{3}$ of the total length of the median $PM$.

Step-by-Step Calculation

$\text{Length of } OM = \frac{1}{3} \times \text{Length of } PM$

$\text{Length of } OM = \frac{1}{3} \times 15\text{ cm} = 5\text{ cm}$

Answer

The correct option is 5 cm (Option c).