A circular park of radius 20m is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other. Find the length of the string of each phone.
Given:
A circular park of radius $20\ m$ is situated in a colony. Three boys Ankur, Amit and Anand are sitting at an equal distance on its boundary each having a toy telephone in his hands to talk to each other.
To do:
We have to find the length of the string of each phone.
Solution:
The radius of the circular park $= 20\ m$
Ankur, Amit and Anand are sitting at equal distances from each other.
By joining the points, an equilateral triangle $ABC$ is formed.
Produce $BO$ to $L$ which is the perpendicular bisector of $AC$.
Therefore,
$BL = 20 + 10$
$= 30\ m$ ($O$ is the centroid of $\triangle ABC$)
Let $a$ be the side of $\triangle ABC$
$\Rightarrow \frac{\sqrt{3}}{2} a=30$
$a=\frac{30 \times 2}{\sqrt{3}}$
$a=\frac{60 \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}}$
$a=\frac{60 \times \sqrt{3}}{3}$
$a=20 \sqrt{3} \mathrm{~m}$
Hence the distance between each other is $20\sqrt3\ m$.
Related Articles
- A circular park of radius \( 20 \mathrm{~m} \) is situated in a colony. Three boys Ankur, Syed and David are sitting at equal distance on its boundary each having a toy telephone in his hands to talk each other. Find the length of the string of each phone.
- A circular park of radius $40\ m$ is situated in a colony. Three boys Ankur, Amit and Anand are sitting at equal distance on its boundary each having a toy telephone in his hands to talk to each other. Find the length of the string of each phone.
- Show that the diagonals of a square are equal and bisect each other at right angles.
- A milkman sold two of his buffaloes for Rs.\( \ 20,000 \) each. On one he made a gain of \( 5 \% \) and on the other a loss of \( 10 \% \). Find his overall gain or loss. (Hint: Find CP of each)
- It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters $16\ m$ and $12\ m$ in a locality. Find the radius of the new park.
- Check if all rows of a matrix are circular rotations of each other in Python
- Each side of a rhombus is 10 cm. If one of its diagonals is 16 cm find the length of the other diagonal.
- Show thal if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.
- Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.
- Draw a pair of tangents to a circle of radius 3 cm, which are inclined to each other at the angle of $60^{o}$.
- A wooden toy was made by scopoping out a hemisphere of same radius from each end of a solid cylinder.If the height of the cylinder is $10\ cm$, and its base is of radius $3.5\ cm$, find the volume of wood in the toy. [ use $\pi =\frac{22}{7}$]
- A car travels 1 kilometre distance in which each wheel makes 450 complete revolutions. Find the radius of its wheels.
- The length of a diagonal of a square is 8. Find the length of each side of the square.
- Four equal circles, each of radius a, touch each other. Show that the area between them is \( \frac{6}{7} a^{2} \cdot( \) Take \( \pi=22 / 7) \)
- JavaScript Program to Check if all rows of a matrix are circular rotations of each other
Kickstart Your Career
Get certified by completing the course
Get Started