Bidyut Guha Thakurta and Amitava Mitra Solutions for Exercise 1: EXERCISE 7

Construct a square each of whose side is $\sqrt{20} \mathrm{cm}$.

Find the square root of $20$ by geometric method.

Construct an equilateral triangle of side $7 \mathrm{cm}$. Then, draw an incircle of this triangle. 

Find the value of $2\sqrt{7}$ by geometric method.

Construct a circle of radius $2.6 \mathrm{cm}$ and draw a tangent at any point on the circle.

Draw a circle with radius $2.5 \mathrm{cm}$ and draw a tangent to the circle from a point outside the circle at a distance $6.5 \mathrm{cm}$ from the centre and find the length of the tangent. 

Construct a circle with centre $O$ and radius $2.5 \mathrm{cm}$. Take a point $P$ at a distance $7 \mathrm{cm}$ from $O$. Draw two tangents to the circle from $P$.

Construct a circle with radius $4.5 \mathrm{cm}$ and draw two tangents to the circle from the external point at a distance $7.5 \mathrm{cm}$ from the centre. Find the length of the tangents and find the relation between them.