Suppose $∆ABC$ is an isosceles triangle with $\angle C=90°,A=\left(2,3\right)$ and $B=\left(4,5\right)$. Then the centroid of the triangle is

The measures of the sides of a triangle are 7, 8 and 9 cm. Find the length of the largest side of a similar triangle whose shortest side is 35 cm. 

(A) 55 cm 

(B) 40 cm 

(C) 45 cm 

(D) 50 cm 

The angles of a triangle are in the ratio of 1 : 2 : 3. What is the measure of the smallest angle (in degrees)?

Consider the following figure shown below and choose which of the following equation is CORRECT about the similarity of both triangles?

Let $ABC$ be a triangle and $M$ be a point on side $AC$ closer to vertex $C$ than $A$. Let $N$ be a point on side $AB$ such that $MN$ is parallel to $BC$ and let $P$ be a point  on side $BC$ such that $MP$ is parallel to $AB$. If the area of the quadrilateral $BNMP$ is equal to $\frac{5}{18}$ of the area of $\mathrm{\Delta }ABC$, then the ratio $AM/MC$ equals