Mahabir Singh Solutions for Chapter: Triangles, Exercise 3: ACHIEVERS SECTION (HOTS)

In the given figure, $ABC$ is a right triangle right-angled at $B$. $AD$ and $CE$ are the two medians drawn from $A$ and $C$ respectively. If $AC=5 \mathrm{cm}$ and $AD =\frac{3\sqrt{5}}{2}\mathrm{cm}$, then the length of $CE$ is 

Match the following

Which of the statement is correct

$P$ and $Q$ are the mid-points of the sides $CA$ and $CB$ respectively of a $△ABC$, right angled at $C$, then find:

(i) $4A{C}^2+B{C}^2$

(ii) $4B{C}^2+A{C}^2$

(iii) $4\left(A{Q}^2+B{P}^2\right)$

In the given figure, the line segment $XY$is parallel to side $AC$of $△ABC$and it divides the triangle into two parts of equal area. Then, find

(i) $AX:AB$

(ii) $\frac{AC}{XY}$