The length of the tangent drawn from a point P to a circle of radius 2.5 cm is 6 cm. What is the shortest distance from point P to the circle.?
A. 2
B. 2.5
C. 3
D. 3.5
E. 4
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
The length of the tangent drawn from a point P to a circle o
This topic has expert replies
-
gmatter2012
- Master | Next Rank: 500 Posts
- Posts: 134
- Joined: Sat May 05, 2012 7:03 pm
- Thanked: 1 times
-
gmatter2012
- Master | Next Rank: 500 Posts
- Posts: 134
- Joined: Sat May 05, 2012 7:03 pm
- Thanked: 1 times
I know this looks easy , how to calculate square root(42.25)
because : 6^2 + 2.5^2 = H^2 using Pythagoras theorem so H = square root( 36+ 6.25) = sqrroot( 42.25)
answer would of course be H - 2.5
because : 6^2 + 2.5^2 = H^2 using Pythagoras theorem so H = square root( 36+ 6.25) = sqrroot( 42.25)
answer would of course be H - 2.5
GMAT/MBA Expert
-
Anurag@Gurome
- GMAT Instructor
- Posts: 3835
- Joined: Fri Apr 02, 2010 10:00 pm
- Location: Milpitas, CA
- Thanked: 1854 times
- Followed by:523 members
- GMAT Score:770
gmatter2012 wrote:The length of the tangent drawn from a point P to a circle of radius 2.5 cm is 6 cm. What is the shortest distance from point P to the circle?
We need to find the length of PD.
Now, OP = OD = 2.5 cm and PT = 6 cm
And, OP² = (OT² + PT²)
---> (OD + PD)² = (OT² + PT²)
---> (OD² + 2*OD*PD + PD²) = (OT² + PT²)
---> (2.5² + 2*2.5*PD + PD²) = (2.5² + 6²)
---> (PD² + 5PD) = 6²
---> (PD² + 5PD - 36) = 0
---> (PD - 4)(PD + 9) = 0
As length of a line segment cannot be negative, PD must be equal to 4
The correct answer is E.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
GMAT/MBA Expert
-
Anurag@Gurome
- GMAT Instructor
- Posts: 3835
- Joined: Fri Apr 02, 2010 10:00 pm
- Location: Milpitas, CA
- Thanked: 1854 times
- Followed by:523 members
- GMAT Score:770
You don't need to find the exact value if you proceed this way.gmatter2012 wrote:I know this looks easy , how to calculate square root(42.25)
because : 6^2 + 2.5^2 = H^2 using Pythagoras theorem so H = square root( 36+ 6.25) = sqrroot( 42.25)
answer would of course be H - 2.5
--> √36 < √42.25 < √49
--> 6 < √42.25 < 7
--> (6 - 2.5) < (√42.25 - 2.5) < (7 - 2.5)
--> 3.5 < (√42.25 - 2.5) < 4.5
Only option that lies between 3.5 and 4.5 is option E.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
-
gmat_and_me
- Senior | Next Rank: 100 Posts
- Posts: 58
- Joined: Sat Mar 05, 2011 9:14 am
- Location: Bangalore
- Thanked: 20 times
- Followed by:5 members
- GMAT Score:770
Well, let's just remove the decimal for now. What is asked is root of 4225.
We know that this value falls between 3600 (60^2) and 4900(70^2). Assuming
that GMAT provides us with good numbers, the one and only number whose
square can result in 5 in the units place is 65. So the root of 42.25 has to be
6.5.
There is an easier way to find square of a number ending with 5. The square
will always end in 25. The most significant number will be equal to the square
of the rest of the digits added with the rest of the digit. For e.g.: 15^2. Result
will end in 25. What is left is 1. Square of 1 + 1 = 2. So square = 225. What
about 65. Result will end with 25. The most significant digits will be 6^2 + 6 = 42.
So the result is 4225.
HTH
We know that this value falls between 3600 (60^2) and 4900(70^2). Assuming
that GMAT provides us with good numbers, the one and only number whose
square can result in 5 in the units place is 65. So the root of 42.25 has to be
6.5.
There is an easier way to find square of a number ending with 5. The square
will always end in 25. The most significant number will be equal to the square
of the rest of the digits added with the rest of the digit. For e.g.: 15^2. Result
will end in 25. What is left is 1. Square of 1 + 1 = 2. So square = 225. What
about 65. Result will end with 25. The most significant digits will be 6^2 + 6 = 42.
So the result is 4225.
HTH
gmatter2012 wrote:I know this looks easy , how to calculate square root(42.25)
because : 6^2 + 2.5^2 = H^2 using Pythagoras theorem so H = square root( 36+ 6.25) = sqrroot( 42.25)
answer would of course be H - 2.5
-
gmatter2012
- Master | Next Rank: 500 Posts
- Posts: 134
- Joined: Sat May 05, 2012 7:03 pm
- Thanked: 1 times
gmatter2012 wrote:I know this looks easy , how to calculate square root(42.25)
because : 6^2 + 2.5^2 = H^2 using Pythagoras theorem so H = square root( 36+ 6.25) = sqrroot( 42.25)
answer would of course be H - 2.5
This is really smart !Anurag@Gurome wrote:
You don't need to find the exact value if you proceed this way.
--> √36 < √42.25 < √49
--> 6 < √42.25 < 7
--> (6 - 2.5) < (√42.25 - 2.5) < (7 - 2.5)
--> 3.5 < (√42.25 - 2.5) < 4.5
Only option that lies between 3.5 and 4.5 is option E.
Thank you.gmat_and_me wrote: Well, let's just remove the decimal for now. What is asked is root of 4225.
We know that this value falls between 3600 (60^2) and 4900(70^2). Assuming
that GMAT provides us with good numbers, the one and only number whose
square can result in 5 in the units place is 65. So the root of 42.25 has to be
6.5.
There is an easier way to find square of a number ending with 5. The square
will always end in 25. The most significant number will be equal to the square
of the rest of the digits added with the rest of the digit. For e.g.: 15^2. Result
will end in 25. What is left is 1. Square of 1 + 1 = 2. So square = 225. What
about 65. Result will end with 25. The most significant digits will be 6^2 + 6 = 42.
So the result is 4225.
