Difference between revisions of "1993 IMO Problems/Problem 2"
William122 (talk | contribs) |
(→Problem) |
||
| (2 intermediate revisions by one other user not shown) | |||
| Line 1: | Line 1: | ||
| + | ==Problem== | ||
| + | |||
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}{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. | |
| − | + | ||
| + | == Solution == | ||
| + | {{solution}} | ||
| + | |||
| + | ==See Also== | ||
| + | |||
| + | {{IMO box|year=1993|num-b=1|num-a=3}} | ||
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
This problem needs a solution. If you have a solution for it, please help us out by adding it.
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 | ||
