Question : $\triangle ABC$ is an equilateral triangle with a side of 12 cm and AD is the median. Find the length of GD if G is the centroid of $\triangle ABC$.

Option 1: $6 \sqrt{3}$ cm

Option 2: $3 \sqrt{3} $ cm

Option 3: $4 \sqrt{3} $ cm

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

Question : The side of an equilateral triangle is 12 cm. What is the radius of the circle circumscribing this equilateral triangle?

Option 1: $6 \sqrt{3}\ \text{cm}$

Option 2: $4\sqrt{3}\ \text{cm}$

Option 3: $9 \sqrt{3}\ \text{cm}$

Option 4: $5\sqrt{3}\ \text{cm}$

Question : The side of an equilateral triangle is 9 cm. What is the radius of the circle circumscribing this equilateral triangle?

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

Option 2: $5\sqrt{3}$ cm

Option 3: $4\sqrt{3}$ cm

Option 4: $3\sqrt{3}$ cm

Question : ABC is an isosceles right-angle triangle. $\angle ABC = 90 ^{\circ}$ and AB = 12 cm. What is the ratio of the radius of the circle inscribed in it to the radius of the circle circumscribing $\triangle ABC$?

Option 1: $6–\sqrt{2}: 3 \sqrt{2}$

Option 2: $2–\sqrt{2}: \sqrt{2}$

Option 3: $6–3 \sqrt{2}: 1 \sqrt{2}$

Option 4: $6–3 \sqrt{2}: 6 \sqrt{2}$

Question : The side of an equilateral triangle is 36 cm. What is the radius of the circle circumscribing this equilateral triangle?

Option 1: $13 \sqrt{3} \mathrm{~cm}$

Option 2: $10 \sqrt{3} \mathrm{~cm}$

Option 3: $12 \sqrt{3} \mathrm{~cm}$

Option 4: $9 \sqrt{3} \mathrm{~cm}$