Question : If ABC is an equilateral triangle and D is a point in BC such that AD is perpendicular to BC, then:

Option 1: AB : BD = 1 : 1

Option 2: AB : BD = 1 : 2

Option 3: AB : BD = 2 : 1

Option 4: AB : BD = 3 : 2

Question : Three medians AD, BE, and CF of $\triangle ABC$ intersect at G. The area of $\triangle ABC$ is $36\text{ cm}^2$. Then the area of $\triangle CGE$ is:

Option 1: $12\text{ cm}^2$

Option 2: $6\text{ cm}^2$

Option 3: $9\text{ cm}^2$

Option 4: $18\text{ cm}^2$

Question : G and AD are respectively the centroid and median of the triangle $\triangle$ABC. The ratio AG : AD is equal to:

Option 1: 3 : 2

Option 2: 2 : 3

Option 3: 2 : 1

Option 4: 1 : 2

Question : In $\triangle$ABC, the bisector of $\angle$BAC intersects BC at D and the circumcircle of $\triangle$ABC at E. If AB : AD = 3 : 5, then AE : AC is:

Option 1: 5 : 3

Option 2: 3 : 2

Option 3: 2 : 3

Option 4: 3 : 5

Question : G is the centroid of $\triangle$ABC. If AG = BC, then measure of $\angle$BGC is:

Option 1: 45°

Option 2: 60°

Option 3: 90°

Option 4: 120°