Nishit K Sinha Solutions for Chapter: Measurement, Exercise 1: Practice Exercises

The sides of a regular octagon are extended to form a star. Find the measure of the internal angle at each point of the star.

Let $\mathrm{ABCDEF}$ be a regular hexagon. What is the ratio of the area of the triangle $\mathrm{ACE}$to that of the hexagon $\mathrm{ABCDEF}$?

The line AB is $6 \mathrm{m}$ in length and is the tangent to the inner one of the two concentric circles at point C. It is known that the radii of the two circles are integers. The radius of the outer circle is

Two chords of lengths a and b of a circle subtend$60°$ and $90°$ angles at the centre, respectively. Which of the following is correct?

What is the distance in cm between two parallel chords of lengths $32 \mathrm{cm}$ and $24 \mathrm{cm}$ in a circle of radius$20 \mathrm{cm}$?

Four points$\mathrm{A}, \mathrm{B}, \mathrm{C}$ and $\mathrm{D}$lie on a straight line in the $\mathrm{X} - \mathrm{Y}$ plane, such that$\mathrm{AB} = \mathrm{BC} = \mathrm{CD},$ and the length of $\mathrm{AB}$ is $1 \mathrm{metre}$. An ant at $\mathrm{A}$ wants to reach a sugar particle at $\mathrm{D}$. But there are insect repellents kept at points $\mathrm{B}$ and $\text{C}$. The ant would not go within one metre of any insect repellent. The minimum distance in metres the ant must traverse to reach the sugar particle is

Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal and saved a distance equal to half the longer side. Then the ratio of the shorter side to the longer side is

If $\mathrm{a}, \mathrm{b}$ and $\mathrm{c}$ are the sides of a triangle, and ${\mathrm{a}}^2+{\mathrm{b}}^2$ $=\mathrm{b} \mathrm{c}+\mathrm{c} \mathrm{a}+\mathrm{a} \mathrm{b}$, then the triangle is