Question : If two medians BE and CF of a triangle ABC, intersect each other at G and if BG = CG, $\angle$BGC = $120^{\circ}$, BC = 10 cm, then the area of the triangle ABC is:

Option 1: $50\sqrt{3}$ $cm^2$

Option 2: $60$ $cm^2$

Option 3: $25$ $cm^2$

Option 4: $25\sqrt{3}$ $cm^2$

Question : For a triangle ABC, D and E are two points on AB and AC such that $\mathrm{AD}=\frac{1}{6} \mathrm{AB}$, $\mathrm{AE}=\frac{1}{6} \mathrm{AC}$. If BC = 22 cm, then DE is _______. (Consider up to two decimals)

Option 1: 1.33 cm

Option 2: 1.67 cm

Option 3: 3.67 cm

Option 4: 3.33 cm

Question : In $\triangle \mathrm{ABC}$, AB = AC, and D is a point on side AC such that BD = BC. If AB = 12.5 cm and BC = 5 cm, then what is the measure of DC?

Option 1: 2 cm

Option 2: 2.5 cm

Option 3: 3 cm

Option 4: 1.8 cm

Question : Let $\triangle ABC \sim \triangle RPQ$ and $\frac{{area}(\triangle {ABC})}{{area}(\triangle {PQR})}=\frac{4}{9}$. If AB = 3 cm, BC = 4 cm and AC = 5 cm, then RP (in cm) is equal to:

Option 1: 6

Option 2: 5

Option 3: 4.5

Option 4: 12

Question : In $\triangle$ ABC, $\angle$ BCA = $90^{\circ}$, AC = 24 cm and BC = 10 cm. What is the radius (in cm) of the circumcircle of $\triangle$ ABC?

Option 1: 12.5

Option 2: 13

Option 3: 25

Option 4: 26