If a circle passes through points (1, 2)(2,5),and (5,4) what is the diameter of the circle?
(A) sqrt(18)
(B) sqrt(20)
(C) sqrt(22)
(D) sqrt(26)
(E) sqrt(30)
Circle
This topic has expert replies
- thephoenix
- Legendary Member
- Posts: 1560
- Joined: Tue Nov 17, 2009 2:38 am
- Thanked: 137 times
- Followed by:5 members
IMO B
let the centre be x,y
eqn 1(dist b/n center and point 1,2) is x
x^2+1-2x+y^2+4-4y
similarly eqn2 x^2+y^2+25+4-10y-4x
eqn3 x^2+y^2+25+16-10x-8y
by equating eqn 1 and 2 we get x+3y=12
and by equating eqn2 and 3 we get 3x-y=6solving x=y=3
radius=sqrt5 and dia=sqrt20
let the centre be x,y
eqn 1(dist b/n center and point 1,2) is x
x^2+1-2x+y^2+4-4y
similarly eqn2 x^2+y^2+25+4-10y-4x
eqn3 x^2+y^2+25+16-10x-8y
by equating eqn 1 and 2 we get x+3y=12
and by equating eqn2 and 3 we get 3x-y=6solving x=y=3
radius=sqrt5 and dia=sqrt20
Many of the great achievements of the world were accomplished by tired and discouraged men who kept on working
- harshavardhanc
- Legendary Member
- Posts: 526
- Joined: Sat Feb 21, 2009 11:47 pm
- Location: India
- Thanked: 68 times
- GMAT Score:680
couldn't find a shorter way, but to solve the equations.getso wrote:If a circle passes through points (1, 2)(2,5),and (5,4) what is the diameter of the circle?
(A) sqrt(18)
(B) sqrt(20)
(C) sqrt(22)
(D) sqrt(26)
(E) sqrt(30)
![Sad :(](./images/smilies/sad.png)
IMO B.
Anyone with a short-cut ?
Regards,
Harsha
Harsha
-
- Legendary Member
- Posts: 576
- Joined: Sat Mar 13, 2010 8:31 pm
- Thanked: 97 times
- Followed by:1 members
the three points (1, 2)(2,5),and (5,4) form a right angle triangle
distance between (1, 2)(2,5)= V10
distance between (2,5)(5,4)= V10
distance between (1, 2)(5,4)= V20
hence diameter = length of hypotenuse =sqrt(20)
option B
distance between (1, 2)(2,5)= V10
distance between (2,5)(5,4)= V10
distance between (1, 2)(5,4)= V20
hence diameter = length of hypotenuse =sqrt(20)
option B
"If you don't know where you are going, any road will get you there."
Lewis Carroll
Lewis Carroll
-
- Legendary Member
- Posts: 610
- Joined: Fri Jan 15, 2010 12:33 am
- Thanked: 47 times
- Followed by:2 members
If you plot the point on a graph
A (1,2) , B ( 2,5) and C ( 5,4) it becomes clear AB is perpendicular to BC.
Not convinced, slope of AB*slope of BC = -1
(5-2)/(2-1) x(5-4)/(2-5)=-1
Since the circle touch all the points of the triangle ABC and <ABC is 90°
AC has to be the diameter.
AC² = (5-1)²+(4-2)² = 20
IMO B.
Frankly if ABC is not a rt. angle triangle finding the diameter will test concepts beyond the scope of GMAT.
A (1,2) , B ( 2,5) and C ( 5,4) it becomes clear AB is perpendicular to BC.
Not convinced, slope of AB*slope of BC = -1
(5-2)/(2-1) x(5-4)/(2-5)=-1
Since the circle touch all the points of the triangle ABC and <ABC is 90°
AC has to be the diameter.
AC² = (5-1)²+(4-2)² = 20
IMO B.
Frankly if ABC is not a rt. angle triangle finding the diameter will test concepts beyond the scope of GMAT.
- harshavardhanc
- Legendary Member
- Posts: 526
- Joined: Sat Feb 21, 2009 11:47 pm
- Location: India
- Thanked: 68 times
- GMAT Score:680
naaaaaaice! thanks buddy!liferocks wrote:the three points (1, 2)(2,5),and (5,4) form a right angle triangle
distance between (1, 2)(2,5)= V10
distance between (2,5)(5,4)= V10
distance between (1, 2)(5,4)= V20
hence diameter = length of hypotenuse =sqrt(20)
option B
Regards,
Harsha
Harsha
-
- Legendary Member
- Posts: 2326
- Joined: Mon Jul 28, 2008 3:54 am
- Thanked: 173 times
- Followed by:2 members
- GMAT Score:710
https://www.codecogs.com/reference/maths ... circle.phpliferocks wrote:the three points (1, 2)(2,5),and (5,4) form a right angle triangle
distance between (1, 2)(2,5)= V10
distance between (2,5)(5,4)= V10
distance between (1, 2)(5,4)= V20
hence diameter = length of hypotenuse =sqrt(20)
option B
Guys, i think are we writing olympiads....?? hehehe!
Thanks for the wonderful explaination..kstv wrote:If you plot the point on a graph
A (1,2) , B ( 2,5) and C ( 5,4) it becomes clear AB is perpendicular to BC.
Not convinced, slope of AB*slope of BC = -1
(5-2)/(2-1) x(5-4)/(2-5)=-1
Since the circle touch all the points of the triangle ABC and <ABC is 90°
AC has to be the diameter.
AC² = (5-1)²+(4-2)² = 20
IMO B.
Frankly if ABC is not a rt. angle triangle finding the diameter will test concepts beyond the scope of GMAT.
- shashank.ism
- Legendary Member
- Posts: 1022
- Joined: Mon Jul 20, 2009 11:49 pm
- Location: Gandhinagar
- Thanked: 41 times
- Followed by:2 members
nice one..kstv wrote:If you plot the point on a graph
A (1,2) , B ( 2,5) and C ( 5,4) it becomes clear AB is perpendicular to BC.
Not convinced, slope of AB*slope of BC = -1
(5-2)/(2-1) x(5-4)/(2-5)=-1
Since the circle touch all the points of the triangle ABC and <ABC is 90°
AC has to be the diameter.
AC² = (5-1)²+(4-2)² = 20
IMO B.
Frankly if ABC is not a rt. angle triangle finding the diameter will test concepts beyond the scope of GMAT.
My Websites:
www.mba.webmaggu.com - India's social Network for MBA Aspirants
www.deal.webmaggu.com -India's online discount, coupon, free stuff informer.
www.dictionary.webmaggu.com - A compact free online dictionary with images.
Nothing is Impossible, even Impossible says I'm possible.
www.mba.webmaggu.com - India's social Network for MBA Aspirants
www.deal.webmaggu.com -India's online discount, coupon, free stuff informer.
www.dictionary.webmaggu.com - A compact free online dictionary with images.
Nothing is Impossible, even Impossible says I'm possible.