A man travels 10 meter towards east from point A to point B, then he turns left for 10 m from point

M4maths Previous Puzzles

20 Jan 2015 Radius of semicircular path

A man travels 10 meter towards east from point A to point B, then he turns left for 10 m from point B to point C. From point C it starts to move in a semicircle CXD. CD is perpendicular to BC and D is towards east relative to C. If his distance at D from initial point
A is 50 m, then radius of semicircle path will be

OPtion

1) 5*Sqrt(3) - 5
2) 20*Sqrt(6) - 10
3) 10*Sqrt(6) - 5
4) 5*Sqrt(6) - 10
5) 20*Sqrt(6) - 20
6) 40
7) 20
8) 5*Sqrt(6) - 5
9) 10*Sqrt(3) - 10
10)10*

Solution

According to given condition
Net distance of man along east = 10 + 2R
Net distance of man along north = 10
So
10^2 + (10+2R)^2 = 50^2
10 + 2R = Sqrt(2400)
2R = 10*Sqrt(24) - 10
R = 5*Sqrt(24) - 5
R = 10*Sqrt(6) - 5

Option 3)

Correct Option: 3 Best Solution (27)

Supriya Mondal   9 years AGO

Let the radius is x m
Then we can write,
10*10+(10+2x)*(10+2x)=50*50
So, 10+2x=sqrt(50*50-10*10)
Then,2x=sqrt(2400)-10
Then, x=sqrt(600)-5
Then, x=10*sqrt(6)-5
So option 3) 10*sqrt(6)-5 is the right answer

Like? Yes (3) | No   

NARESH AVIRENU   9 years AGO

from given data

AB=10 mt
BC=10 mt
AD=50 mt

(50)^2 = (10)^2 + (10+y)^2

2500 = 100+(10+y)^2
=> y = 20*Sqrt(6) - 10

radius of the semi circle =y/2
so,
= (20*Sqrt(6) - 10)/2

radius of semi circle is = 10*Sqrt(6) - 5.

=

Like? Yes (3) | No   

Yekollu Muneeswar   9 years AGO

sketch diagram from there you will get,
50^2= 10^2+x^2 ==> x=sqrt(2400)

radius=(x-10)/2
==> 10sqrt(6)-5

ans 3)

Like? Yes (2) | No   

Mahesh   9 years AGO

The distance between the starting point and ending point is given as 50
The vertical distance is 10
horizantal distance can be obtained by applying pythagoras theoram
It will be 50^2 - 10^2 under root
So, it will be root 2400
Now horizantal distance is 10 + diameter of the circle
so diammeter of the circle is root 2400 -10 = 20 root 6 - 10
Radius of circle is 10 root 6 - 5

Like? Yes (1) | No   

RAKESH   9 years AGO

(10+x)^2 + 10^2 = 50^2
=> x = (20*sqrt6 - 10)

radius = x/2 = 10*Sqrt(6) - 5

Like? Yes (1) | No   

Nupur   9 years AGO

On making the pictoral diagram we realize that the mathematical equation obtained is:
Taking diameter = x
50^2 = 10^2 + (10-x)^2

Solving we get x = -10+ 20*sqrt(6)

Hence radius = x/2

Like? Yes (1) | No   

ABHINAV PUSHPAM   9 years AGO

50^2 = 10^2+(10+x)^2
after solving
x= - 10(1-2sqrt(6))
radius of semi circular path is r=x=2
10sqrt(6)- 5
option 3). is correct

Like? Yes (1) | No   

MRITUNJAY   9 years AGO

50^2 = 10^2+(10+x)^2
after solving
x= - 10(1-2sqrt(6))
radius of semi circular path is r=x=2
10sqrt(6)- 5
option 3.

Like? Yes (1) | No   

MRITUNJAY KUMAR   9 years AGO

Option)3

Like? Yes (1) | No   

Sravanthi   9 years AGO

radius is CD/2.

Like? Yes (1) | No   

khushboo goenka   9 years AGO

(10+2r)^2 +10^2=50^2

Like? Yes (1) | No   

Anshul Garg   9 years AGO

According to the question,
if we draw the sketch and find the relationship,
we have
(x+10)^2 + 10^2 = 50^2 (x is the diameter of the semicircle.) (And this relationship came from pythagoras theorem)

After Solving the equation, we have x^2 + 20x - 2300 = 0
It gives
x = (-20 + 40*sqrt(6))/2
and (-20 - 40*sqrt(6))/2
But we will neglect second option (because length can't be negative)
So , x = -10 + 20*sqrt(6)
And the radius of semicircle would be =
x/2 => 10*sqrt(6) - 5

Like? Yes (1) | No   

arush gupta   9 years AGO

ans (20sqrt(6)-10)/2=10sqrt(6)-5

Like? Yes (1) | No   

apurva katyayni   9 years AGO

10^2 + (10+x)^2 = 50^2
(10 +x)^2 = 2400
10+x = 20*sqrt6
x=20sqrt6 -10
radius = x/2= optin 3

Like? Yes (1) | No   

Swathy Murugan   9 years AGO

circumference of semicircle=pi*d
total distance=50
where 20m is straight line and 30 m forms the circumference of semicircle
30=pi*d (d=r/2)
solving this we get 19.10 approximately so the suitable option in the given choice is 3

Like? Yes (1) | No   

mithilesh kumar   9 years AGO

10*SQRT(6)-10

Like? Yes (1) | No   

abhilasha   9 years AGO

this is the correct ans. pi * r = 30

Like? Yes (1) | No   

Jigyasa Kumar   9 years AGO

pi*r = 30
so this is the answer..

Like? Yes (1) | No   

shreyansh pandey   9 years AGO

extend CD to a point E towards west relative to C where CE = 10 m than it forms an right angle triangle AED where
AE = 10m
AD = 50m
thus radius = 1/2 *(sqrt(50^2 - 10^2)-10)
= 10sqrt(6)-5

Like? Yes (1) | No   

Akshat Mokashi   9 years AGO

This is the right answer

Like? Yes (1) | No   

A M ANKIT KALLURAYA   9 years AGO

the sum of square of twice the radius of semicircle and AB with the sum of square of BC equates to AD square distance...
we get r=-5+10sqrt6

Like? Yes (1) | No   

Niraj Agarwal   9 years AGO

Extend line AB and Draw a straight line from D onto the extended AB and name the end point as E.

Now, taking the triangle AED into consideration we can conclude that,

Sin (theta) = 10/50 = 1/5
Hence, cos (theta) = sqrt(24)/5 = 2*sqrt(6) / 5 -------- (1)

Also, from the triangle we have
cos (theta) = (10 + 2r) / 50 --------- (2)

Equating (1) and (2), we get
r = 10 * sqrt(6) - 5

Like? Yes (1) | No   

Mohd Belal   9 years AGO

Here i have considered the displacement of D from point A.
But instead it was mentioned as the distance.. keeping the distance as 50 will result the answer as 30/3.14 , but it was nit present in the options.
So rather the displacement concept of point D from A was 50 is to be taken and answer is option 3.

Like? Yes (1) | No   

sayantani jana   9 years AGO

50^2=x^2+10^2
x=20*sqrt(6)
then
radius=(20sqrt(6)-10)/2

Like? Yes (1) | No   

Ajinkya Kulkarni   9 years AGO

X^2+20x-2300=0

Like? Yes (1) | No (1)  

P ANAND   9 years AGO

i did it

Like? Yes (1) | No (2)  

Surit Datta   9 years AGO

Option 3 is the answer.
That's it.

Like? Yes (1) | No (2)