Difference between revisions of "1962 IMO Problems/Problem 6"

(New page: ==Problem== Consider an isosceles triangle. Let <math>r</math> be the radius of its circumscribed circle and <math>\rho</math> the radius of its inscribed circle. Prove that the distance <...)
 
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==Problem==
 
==Problem==
 
Consider an isosceles triangle. Let <math>r</math> be the radius of its circumscribed circle and <math>\rho</math> the radius of its inscribed circle. Prove that the distance <math>d</math> between the centers of these two circles is  
 
Consider an isosceles triangle. Let <math>r</math> be the radius of its circumscribed circle and <math>\rho</math> the radius of its inscribed circle. Prove that the distance <math>d</math> between the centers of these two circles is  
<center><math>d=\sqrt{r(r-2p)}</math>.</center>
+
<center><math>d=\sqrt{r(r-2\rho)}</math>.</center>
  
 
==Solution==
 
==Solution==

Revision as of 11:35, 16 February 2009

Problem

Consider an isosceles triangle. Let $r$ be the radius of its circumscribed circle and $\rho$ the radius of its inscribed circle. Prove that the distance $d$ between the centers of these two circles is

$d=\sqrt{r(r-2\rho)}$.

Solution

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See Also

1962 IMO (Problems) • Resources
Preceded by
Problem 5
1 2 3 4 5 6 Followed by
Problem 7
All IMO Problems and Solutions
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