Prove that the locus of a point equidistant from the extremities a line segment is the perpendicular bisector of it.

If $\mathrm{a}, \mathrm{b}$ and $\mathrm{c}$ are sides of a right triangle where $\mathrm{c}$ is the hypotenuse, prove that the radius of the circle which touches the sides of the triangle is $\mathrm{r}=\frac{\mathrm{a}+\mathrm{b}-\mathrm{c}}{2}$.

Find the value of $\mathrm{x},$ if the mean of the following distribution is $18 .$

In the given figure, chords $\mathrm{AB}$ and $\mathrm{CD}$of the circle are produced to meet at $\mathrm{O}.$Prove that triangles $\mathrm{ODB}$ and $\mathrm{OCA}$ are similar. Given that $\mathrm{CD}=2\mathrm{cm}$ $\mathrm{DO}=6\mathrm{cm}$ and $\mathrm{BO}=3\mathrm{cm},$ calculate $\mathrm{AB}.$ Also find $\frac{\text{ area of quad. CABD }}{\text{ area of }\mathrm{\Delta }\text{ CAO }}.$

If $\mathrm{M}\times \left[\begin{array}{rr}3& 2\\ 2& -1\end{array}\right]=[-1 4];$  find the order of matrix $\mathrm{M}.$

If $\mathrm{M}\times \left[\begin{array}{rr}3& 2\\ 2& -1\end{array}\right]=[-1 4];$  find the matrix $\mathrm{M}.$