To find:
The values of the unknowns.
Solution:
It is known that in a triangle, the centroid divides each median in the ratio of 2:1.
a)
In the first triangle, we have OC : OE = 2:1. So,
[tex]\begin{gathered} \frac{OC}{OE}=\frac{2}{1} \\ \frac{5}{OE}=2 \\ OE=2.5\text{ cm} \end{gathered}[/tex]
And AO : OF = 2:1. SO,
[tex]\begin{gathered} \frac{AO}{OF}=\frac{2}{1} \\ \frac{6}{OF}=2 \\ OF=3\text{ cm} \end{gathered}[/tex]
And BO : OD = 2:1. So,
[tex]\begin{gathered} \frac{BO}{OD}=\frac{2}{1} \\ \frac{BO}{2}=2 \\ BO=4\text{ cm} \end{gathered}[/tex]
Thus, we get BO = 4 cm, OF = 3 cm, EO = 2.5 cm.
b)
In the second triangle, given that AE = 10 cm, DO = 3 cm. Since the centroid divides each median in the ratio of 2:1. SO,
[tex]\begin{gathered} \frac{AO}{OE}=\frac{2}{1} \\ \frac{AO}{AE-AO}=2 \\ \frac{AO}{10-AO}=2 \\ AO=20-2AO \\ 3AO=20 \\ AO=\frac{20}{3} \end{gathered}[/tex]
And OC : DO = 2:1. SO,
[tex]\begin{gathered} \frac{OC}{DO}=\frac{2}{1} \\ \frac{DC-DO}{DO}=2 \\ \frac{DC-3}{3}=2 \\ DC-3=6 \\ DC=9\text{ cm} \end{gathered}[/tex]
Thus, DC = 9 cm, AO = 20/3 cm.
