Difference between revisions of "1962 IMO Problems/Problem 6"
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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 11:35, 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 |