My Math Forum  

Go Back   My Math Forum > High School Math Forum > Geometry

Geometry Geometry Math Forum


Thanks Tree1Thanks
  • 1 Post By v8archie
Reply
 
LinkBack Thread Tools Display Modes
February 6th, 2015, 05:15 PM   #1
Senior Member
 
Joined: Jan 2015
From: USA

Posts: 107
Thanks: 2

Circles impossible problem :(

My teacher went nuts! How do I solve this???

The problem is in the attached picture. Thanx!
Attached Images
File Type: jpg 10965700_10153097926419700_1936437963_n.jpg (22.3 KB, 17 views)
matisolla is offline  
 
February 6th, 2015, 07:33 PM   #2
Math Team
 
Joined: Dec 2013
From: Colombia

Posts: 7,634
Thanks: 2620

Math Focus: Mainly analysis and algebra
Since they are circles, they intersect at zero, one or two points. We are told that it is two. Therefore, you can pick two values for $k$ ($m$ and $n$, for example) and equate the two expressions on the left hand side of the equations.

Equality (for $m \ne n$) will come at precisely two points (independent of $m$ and $n$) which are the solution to our problem.

Alternatively, you can do it by inspection. The term that is independent of $x$ and $y$ is $-(1+k)$. So the other terms must sum to $(1+k)$ in order to satisfy the equation. There are two simple combinations of $x$ and $y$ that do this.

The two points must be equidistant from the centre of the circle. The radius of the circle is minimised when the centre is on the line segment joining the two points.
Thanks from matisolla
v8archie is offline  
Reply

  My Math Forum > High School Math Forum > Geometry

Tags
circles, impossible, problem



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
problem with circles nukem4111 Algebra 0 January 2nd, 2013 07:17 AM
Impossible Math problem bsrecker Algebra 1 October 31st, 2011 04:31 PM
"IMPOSSIBLE PROBLEM" - SEE IF YOU CAN ANSWER IT [reply] s2m0i1t2h Algebra 1 November 24th, 2008 03:46 PM
Trinagle Problem. Math Award Winner Can't Solve, IMPOSSIBLE? nqavisid Algebra 4 November 14th, 2008 12:28 PM
Impossible circle problem g-unitcircle Algebra 4 May 4th, 2007 07:31 AM





Copyright © 2019 My Math Forum. All rights reserved.