Question : In an equilateral triangle, the circumradius is 14 cm. What is the length of the median in this triangle?

Option 1: $14 \sqrt{3} \mathrm{~cm}$

Option 2: $21 \mathrm{~cm}$

Option 3: $18 \sqrt{3} \mathrm{~cm}$

Option 4: $7 \sqrt{3} \mathrm{~cm}$

Question : $\triangle \mathrm {ABC}$ is similar to $\triangle \mathrm{PQR}$ and $\mathrm{PQ}=10 \mathrm{~cm}$. If the area of $\triangle \mathrm{ABC}$ is $32 \mathrm{~cm}^2$ and the area of $\triangle \mathrm{PQR}$ is $50 \mathrm{~cm}^2$, then the length of $A B$ (in $\mathrm{cm}$ ) is equal to:

Option 1: 10

Option 2: 4

Option 3: 6

Option 4: 8

Question : MX is the median of $\triangle M N O$. Y is the centroid of $\triangle M N O$. If YX = 12 cm, then what is the length of MX?

Option 1: 30 cm

Option 2: 36 cm

Option 3: 28 cm

Option 4: 24 cm

Question : In $\triangle$ABC, D is the midpoint of BC. Length AD is 27 cm. N is a point in AD such that the length of DN is 12 cm. The distance of N from the centroid of ABC is equal to:

Option 1: 3 cm

Option 2: 6 cm

Option 3: 9 cm

Option 4: 15 cm

Question : In the isosceles triangle ABC with BC is the unequal side of the triangle, and line AD is the median drawn from the vertex A to the side BC. If the length AC = 5 cm and the length of the median is 4 cm, then find the length of BC (in (cm).

Option 1: 5

Option 2: 3

Option 3: 4

Option 4: 6