$\mathrm{ABC}$ is an equilateral triangle inscribed in a circle with a center $\mathrm{O}$. Radius $\mathrm{OB}=4 \mathrm{cm}$ and $\mathrm{OM}$ is perpenducular to $\mathrm{BC}$. Find $\mathrm{x}$ and the perimeter of the triangle.

 

In the rectangle $\mathrm{ABCD}$, the diagonals intersect at $\mathrm{O}$. If$\angle \mathrm{COD}=120°$ and $\mathrm{AB}=6 \mathrm{cm}$, $\mathrm{OP}$ is perpendicular to $\mathrm{AB}$. Find $\mathrm{x}, \mathrm{y}, \mathrm{BC} \mathrm{and} \mathrm{AC}$.

In the rectangle $PQRS$, $\angle SQR=60°$ and $QR=4 \mathrm{cm}$. Find $SR$ and $QS$

At the base of $∆ABC$ is the rectangle $BCDE$, $CD=3 \mathrm{cm}$, $AC=12 \mathrm{cm}$ and $\angle ACB=30°$. Find the length of $AE$ 

In rectangle $ABCD$, $DB=10 \mathrm{cm}$ and $BC=5 \mathrm{cm}$. Find $\angle BDC$ and the length of $AB$

In a $∆ABC$, $P$ is a point on $AB$ such that $\angle PCB=45°$, $\angle B=90°$ and $\angle ACB=60°$. Find the length of $AP$ if $BC=10 \mathrm{cm}$

In a $∆ABC$, $AD\perp BC$. $BC=100 \mathrm{m}$, $\tan B=\frac{2}{3}$ and $\tan C=\frac{6}{11}$. Find the length of $AD$

Find $x$ and $y$ in the given figure.