The centre of a circle inside a triangle is at a distance of $625 \mathrm{cm}$. from each of the vertices of the triangle. If the diameter of the circle is $350 \mathrm{cm}$. and the circle is touching only two sides of the triangle, find the area of the triangle.

A person is standing at a distance of $1800$meters facing a giant clock at the top of a tower. At $5.00 \mathrm{pm}$., he can see the tip of the minute hand of the clock at $30$degree elevation from his eye-level. Immediately, the person starts walking towards the tower. At $5.10 \mathrm{pm}$., the person noticed that the tip of the minute hand made an angle of $60$degrees with respect to his eye level. Using three-dimensional vision, find the speed at which the person is walking. The length of the minutes hand is $200\sqrt{3}$ meters $(\sqrt{3}=1.732)$.

In the figure below, $\mathrm{AB}=\mathrm{AC}=\mathrm{CD}$. If $\mathrm{ADB}=20°$, what is the value of BAD?

$∆\mathrm{ABC}$ and $\mathrm{\Delta XYZ}$ are equilateral triangles of $54 \mathrm{cm}$ sides. All smaller triangles like $∆\mathrm{ANM},\mathrm{\Delta OCP}$, $\mathrm{\Delta QPX}$ etc are also equilateral triangles. Find the area of the shape MNOPQRM.

Study the figure below and answer the question:

Four persons walk from point A to point D following different routes. The one following ABCD takes $70$ . minutes. Another person takes $45$minutes following ABD. The third person takes $30$minutes following route ACD. The last person takes 65 minutes following route ACBD. If all were to walk at the same speed, how long will it take to go from point B to point C?

In the figure below, two circular curves create $60°$ and $90°$ angles with their respective centers. If the length of the bottom curve Y is $10\mathrm{\pi }$, find the length of the other curve.