Difference between revisions of "1993 IMO Problems/Problem 2"
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Let <math>D</math> be a point inside acute triangle <math>ABC</math> such that <math>\angle ADB = \angle ACB+\frac{\pi}{2}</math> and <math>AC\cdot BD=AD\cdot BC</math>. | Let <math>D</math> be a point inside acute triangle <math>ABC</math> such that <math>\angle ADB = \angle ACB+\frac{\pi}{2}</math> and <math>AC\cdot BD=AD\cdot BC</math>. | ||
| − | (a) Calculate the ratio <math>\frac{AC\cdot CD}{ | + | (a) Calculate the ratio <math>\frac{AC\cdot CD}{AB\cdot BD}</math>. |
(b) Prove that the tangents at <math>C</math> to the circumcircles of <math>\Delta ACD</math> and <math>\Delta BCD</math> are perpendicular. | (b) Prove that the tangents at <math>C</math> to the circumcircles of <math>\Delta ACD</math> and <math>\Delta BCD</math> are perpendicular. | ||
Latest revision as of 23:02, 21 January 2024
Problem
Let 
be a point inside acute triangle 
such that 
and 
.
(a) Calculate the ratio 
.
(b) Prove that the tangents at 
to the circumcircles of 
and 
are perpendicular.
Solution
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See Also
| 1993 IMO (Problems) • Resources | ||
| Preceded by Problem 1 |
1 • 2 • 3 • 4 • 5 • 6 | Followed by Problem 3 |
| All IMO Problems and Solutions | ||
