Using a ruler and a compass only construct a semi-circle with diameter $BC=7cm$. Locate a point $A$ on the circumference of the semi-circle such that $A$ is equidistant from $B$ and $C$. Complete the cyclic quadrilateral $ABCD$, such that $D$ is equidistant from $AB$ and $BC$. Measure $\angle ADC$ and write it down.

Using ruler and compasses only, construct a quadrilateral $\mathrm{ABCD}$ in which $\mathrm{AB}=6 \mathrm{cm},\mathrm{BC}=5 \mathrm{cm},\angle \mathrm{B}=60°,\mathrm{AD}=5 \mathrm{cm}$ and $\mathrm{D}$ is equidistant from $\mathrm{AB}$ and $\mathrm{BC}$. Measure $\mathrm{CD}$.

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 $\mathrm{AB}$.

Use ruler and compasses only for this question. Draw a circle of radius $4 \mathrm{cm}$ and mark two chords $\mathrm{AB}$ and $\mathrm{AC}$ of the circle of length $6 \mathrm{cm}$ and $5 \mathrm{cm}$ respectively.
Construct the locus of points, inside the circle, that are equidistant from $\mathrm{A}$ and $\mathrm{C}$. Prove your construction.
 

Use ruler and compasses only for this question. Draw a circle of radius $4 \mathrm{cm}$ and mark two chords $\mathrm{AB}$ and $\mathrm{AC}$ of the circle of length $6 \mathrm{cm}$ and $5 \mathrm{cm}$ respectively.
Construct the locus of points, inside the circle, that are equidistant from $\mathrm{AB}$ and $\mathrm{AC}$.