EXERCISE

Construct an isosceles triangle $\mathrm{ABC}$such that $\mathrm{AB}=6\mathrm{cm}, \mathrm{BC}=\mathrm{AC}=4\mathrm{cm}.$ Bisect $\angle \mathrm{C}$ internally and mark a point $\mathrm{P}$ on this bisector such that $\mathrm{CP}=5\mathrm{cm}.$ Find the points $\mathrm{Q}$ and $\mathrm{R}$ which are $5\mathrm{cm}$ from $\mathrm{P}$ and also $5\mathrm{cm}$ from the line $\mathrm{AB}.$

Plot the points $\mathrm{A}(2,9),\mathrm{B}(-1,3)$ and $\mathrm{C}(6,3)$ on a graph paper. On the same graph paper, draw the locus of point $\mathrm{A}$ so that the area of $\mathrm{\Delta ABC}$ remains the same as $\mathrm{A}$ moves.

Construct a triangle $\mathrm{BCP}$ given $\mathrm{BC}=5\mathrm{cm},$ $\mathrm{BP}=4\mathrm{cm}$ and $\angle \mathrm{PBC}=45°.$

Complete the rectangle $\mathrm{ABCD}$ such that :

(a) $\mathrm{P}$is equidistant from $\mathrm{AB}$and $\mathrm{BC}.$

(b) $\mathrm{P}$is equidistant from $\mathrm{C}$and$\mathrm{D}.$

Construct a triangle $\mathrm{BCP}$ given $\mathrm{BC}=5\mathrm{cm},$$\mathrm{BP}=4\mathrm{cm}$ and $\angle \mathrm{PBC}=45°.$

Measure and record the length of$\mathrm{AB}.$

Use ruler and compasses only for the following question. All construction lines and arcs must be clearly shown.

Construct a $\mathrm{\Delta ABC}$ in which $\mathrm{BC}=6·5\mathrm{cm},$ $\angle \mathrm{ABC}=60°, \mathrm{AB}=5\mathrm{cm}.$

Use ruler and compasses only for the following question. All construction lines and arcs must be clearly shown.

Construct the locus of points at a distance of $3.5\mathrm{cm}$ from $\mathrm{A}.$

Use ruler and compasses only for the following question. All construction lines and arcs must be clearly shown.

Construct the locus of points equidistant from$\mathrm{AC}$ and $\mathrm{BC}$.

Use raler and compasses only for the following question. All construction lines and arcs must be clearly shown.

Mark $2$points $\mathrm{X}$ and $\mathrm{Y}$ which are at a distance of $3.5\mathrm{cm}$ from $\mathrm{A}$ and also equidistant from $\mathrm{AC}$ and $\mathrm{BC}$. Measure $\mathrm{XY}.$