Question

if ( ts = 3 ), find ( os ).

Explanation:

Step1: Recall the centroid property

In a triangle, the centroid divides each median in a ratio of \(2:1\). Here, \(T\) is the centroid of \(\triangle ONP\) and \(OS\) is a median. So, \(OT = 2TS\) and \(OS=OT + TS\).

Step2: Calculate \(OT\)

Given \(TS = 3\). Since \(OT = 2TS\), then \(OT=2\times3 = 6\).

Step3: Calculate \(OS\)

Since \(OS=OT + TS\), substituting \(OT = 6\) and \(TS = 3\), we get \(OS=6 + 3=9\).

Answer:

\(9\)