R S Aggarwal and Veena Aggarwal Solutions for Exercise 3: TEST YOURSELF

Construct a $∆ABC$ in which $BC=6.5 \mathrm{cm}, AB=4.5 \mathrm{cm}$ and $\angle ABC=60°$. Construct a triangle similar to this triangle whose sides are $\frac{3}{4}$ of the corresponding sides of $∆ABC$.

Construct a $∆ABC$ in which $BC=5 \mathrm{cm}, \angle C={60}^{°}$ and altitude from $A$ equal to $3 \mathrm{cm}$. Construct a $∆ADE$ similar to $∆ABC$ such that each side of $∆ADE$ is $\frac{3}{2}$ times the corresponding side of $∆ABC.$ Write the steps of construction.

Construct an isosceles triangle whose base is $9 \mathrm{cm}$ and altitude $5 \mathrm{cm}$. Construct another triangle whose sides are $\frac{3}{4}$ of the corresponding sides of the first isosceles triangle.

Draw a $∆ABC$, right-angled at $B$ such that $AB=3 \mathrm{cm}$ and $BC=4 \mathrm{cm}$. Now, construct a triangle similar to $∆ABC$, each of whose sides is $\frac{7}{5}$ times the corresponding side of $∆ABC$.

Draw a circle of radius $4.8 \mathrm{cm}$. Take a point $P$ on it. Without using the centre of the circle, construct a tangent at the point $P$. Write the steps of construction.

Draw a circle of radius $3.5 \mathrm{cm}$. Draw a pair of tangents to this circle which are inclined to each other at an angle of $60°$.  Write the steps of construction.

Draw a circle of radius $4 \mathrm{cm}$. Draw tangent to the circle making an angle of $60°$ with a line passing through the centre.

Draw two concentric circles of radii $4 \mathrm{cm}$ and $6 \mathrm{cm}$. Construct a tangent to the smaller circle from a point on the larger circle. Measure the length of this tangent.