1962 IMO Problems/Problem 6: Difference between revisions
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- | <center><math>d=\sqrt{r(r-2\rho)}</math>.</center> | ||
==Solution== | ==Solution== | ||
Revision as of 10:35, 16 February 2009
Problem
Consider an isosceles triangle. Let 
be the radius of its circumscribed circle and 
the radius of its inscribed circle. Prove that the distance 
between the centers of these two circles is
.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 | ||
