EXERCISE

Draw a regular hexagon of side $5\mathrm{cm}.$

Draw a line $\mathrm{AB}=5\mathrm{cm}.$ Mark a point $\mathrm{C}$ on $\mathrm{AB}$ such that $\mathrm{AC}=3\mathrm{cm}.$ Using a ruler and a compass only, construct:

A circle of radius $2.5\mathrm{cm},$ passing through $\mathrm{A}$ and $\mathrm{C}.$

Draw a line $\mathrm{AB}=5\mathrm{cm}.$ Mark a point $\mathrm{C}$ on $\mathrm{AB}$ such that $\mathrm{AC}=3\mathrm{cm}.$ Using a ruler and a compass only, construct:

Construct two tangents to the circle from the external point $\mathrm{B}.$ Measure and record the length of the tangents.

Using a ruler and a compass, construct a triangle $\mathrm{ABC}$ in which $\mathrm{AB}=7\mathrm{cm}, \angle \mathrm{CAB}=60º$ and $\mathrm{AC}=5\mathrm{cm}.$ Construct the locus of points equidistant from $\mathrm{AB}$ and $\mathrm{AC}.$

Using a ruler and a compass, construct a triangle $\mathrm{ABC}$ in which $\mathrm{AB}=7\mathrm{cm}, \angle \mathrm{CAB}=60º$ and $\mathrm{AC}=5\mathrm{cm}.$ Construct the locus of :

Points equidistant from $\mathrm{BA}$ and $\mathrm{BC}.$

Hence construct a circle touching the three sides of the triangle intenally.

Construct a triangle $\mathrm{ABC}$ in which $\mathrm{AB}=5\mathrm{cm}, \mathrm{BC}=6.8\mathrm{cm}$ and median $\mathrm{AD}=4.4\mathrm{cm}.$ Draw incircle of this triangle.

Draw two concentric circles with radii $4\mathrm{cm}$ and $6\mathrm{cm}.$ Taking a point on the outer circle, construct a pair of tangents to inner circle. By measuring the length of both the tangents, show tha they are equal to each other.

In triangle $\mathrm{ABC}, \angle \mathrm{ABC}=90º, \mathrm{AB}=6\mathrm{cm}, \mathrm{BC}=7.2\mathrm{cm}$ and $\mathrm{BD}$ is perpendicular to side $\mathrm{AC}.$ Draw circumcircle of triangle $\mathrm{BDC}$ and then state the length of the radius of this circumcircle drawn.