1975 USAMO Problems/Problem 4
Problem
Two given circles intersect in two points 
and 
. Show how to construct a segment 
passing through and terminating on the two circles such that 
is a maximum.
![[asy] size(150); defaultpen(fontsize(7)); pair A=(0,0), B=(10,0), P=(4,0), Q=(3.7,-2.5); draw(A--B); draw(circumcircle(A,P,Q)); draw(circumcircle(B,P,Q)); label("A",A,(-1,1));label("P",P,(0,1.5));label("B",B,(1,1));label("Q",Q,(-0.5,-1.5)); [/asy]](http://latex.artofproblemsolving.com/c/1/c/c1ce46c52cfe092b52af621b5ca152165e1e7826.png)
Solution posted at
http://www.cut-the-knot.org/wiki-math/index.php?n=MathematicalOlympiads.USA1975Problem4
by Vo Duc Dien
See also
| 1975 USAMO (Problems • Resources) | ||
| Preceded by Problem 3 |
Followed by Problem 5 | |
| 1 • 2 • 3 • 4 • 5 | ||
| All USAMO Problems and Solutions | ||
