V K Raman and S N Sharma Solutions for Exercise 2: EXERCISE 25(B)

$ABCD$ is a parallelogram and the diagonals intersect at $O$ . $AO=(x+3) \mathrm{cm},OC=(2x-6) \mathrm{cm},BO=(y+2) \mathrm{cm}$ and$OD=(2y-14) \mathrm{cm}$. Find the length of the diagonals.

$ABCD$ is a rectangle and the diagonals intersect at $O$. $CA$ and $BD$ are produced to $F,E$ respectively. $\angle OAB=35°$, find the values of $a°,b°,c°,d°,e°$ and $f°$.

$ABCD$ is a rhombus and the diagonals intersect at $O$. Given$\angle OAD=54°$, find the values of $a°,b°,c°,d°,e°$ and $f°$.

$ABCD$ is a rhombus and the diagonals intersect at $O$. Given $AO=(x+ 2) \mathrm{cm}, OC=(2x- 2) \mathrm{cm}, BO=(y+1) \mathrm{cm}$ and$OD=(2y-6) \mathrm{cm}$, find the length of the diagonals.

$ABCD$ is an isosceles trapezium with $AB,CD$ as nonparallel sides. $E$ is the mid-point of $AD$. $B,C$ are joined to $E$. Prove that $\angle ABE=\angle DCE$.

$ABCD$ is a parallelogram and the diagonals intersect at $O$. $E,F$ are the mid-pts of $AO,OC$ respectively. $B$ is joined to $E$ and $D$ is joined to $F$. Prove that $\angle OBE=\angle ODF$.

$ABCD$ is a kite and the diagonals intersect at $O$. Given$\angle ADO=48°$ and $\angle CBO=62°$, find the values of $a°,b°,c°$ and $d°$.

$ABC$ is an equilateral $△$ and $BCDE$ is a square. $A$ is joined to $E$ and $D$. Prove that $\angle BAE=\angle CAD$.