Question : If $AD, BE$ and $CF$ are medians of $\triangle ABC$, then which of the following statement is correct?

Option 1: $(AD + BE + CF) > (AB + BC + CA)$

Option 2: $(AD + BE + CF) < (AB + BC + CA)$

Option 3: $(AD + BE + CF ) =  (AB + BC + CA)$

Option 4: $(AD + BE + CF ) = \sqrt2(AB+BC+CA)$

Question : E is the midpoint of the median AD of $\triangle ABC. BE$ is joined and produced to meet AC at F. F divides AC in ratio:

Option 1: 2 : 3

Option 2: 2 : 1

Option 3: 1 : 3

Option 4: 3 : 2

Question : In $\triangle ABC$, AB = BC = $k$, AC =$\sqrt2k$, then $\triangle ABC$ is a:

Option 1: Isosceles triangle

Option 2: Right-angled triangle

Option 3: Equilateral triangle

Option 4: Right isosceles triangle

Question : In triangle ABC, AD BE and CF are the medians intersecting at point G and the area of triangle ABC is 156 cm². What is the area (in cm²) of triangle FGE?

Option 1: 13

Option 2: 26

Option 3: 39

Option 4: 52

Question : Simplify the following expression.
$(a+b+c)^2-(a-b+c)^2+4ac$

Option 1: $4(bc+ac)$

Option 2: $2(ab+bc+ac)$

Option 3: $4(ab+bc+ac)$

Option 4: $4(bc+ab)$