Jayashri Bhattacharya and Tarika Dhawan Solutions for Exercise 5: Googly

Draw an acute angled triangle $\mathrm{ABC}$. From the vertex $\mathrm{A}$, draw a perpendicular to $\overline{\mathrm{BC}}$ such that the perpendicular cuts $\overline{\mathrm{BC}}$ at $\mathrm{D}$. Measure the length of $\overline{\mathrm{BD}}$ and $\overline{\mathrm{DC}}$.

Draw $\overline{\mathrm{AB}}$ of length $10 \mathrm{cm}$. Construct the perpendicular bisector of $\overline{\mathrm{AB}}$ and name it $\overline{\mathrm{PQ}}$. Take a point $\mathrm{D}$ on $\overline{\mathrm{PQ}}$ and measure the lengths of $\overline{\mathrm{DA}}$ and $\overline{\mathrm{DB}}$.

Draw $\overline{SK}$ of length $4.8 \mathrm{cm}$. Using a ruler and compass, construct a circle whose diameter is equal to $SK$.

Draw an angle $75°$ and find its symmetry.

Draw an angle of measure $140˚$. Divide it into four equal parts using a ruler and compasses.

Construct an angle of $52.5˚$ without using a protractor.

Draw an equilateral triangle using a ruler and compasses. Use the steps of constructing a $60˚$ using a ruler and compasses.

There are two points $\mathrm{A}$ and $\mathrm{B}$. Construct a circle with centre at $\mathrm{A}$ and passing through $\mathrm{B}$. How many such circles can you draw?