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>. | ||
| − | \renewcommand{\labelenumi}{\alph{enumi}} | + | \renewcommand{\labelenumi}{\alph{enumi}.} |
\begin{enumerate} | \begin{enumerate} | ||
\item Calculate the ratio <math>\frac{AC\cdot CD}{AC\cdot BD}</math> | \item Calculate the ratio <math>\frac{AC\cdot CD}{AC\cdot BD}</math> | ||
\item Prove that the tangents at <math>C</math> to the circumcircles of <math>\triangle ACD</math> and <math>\triangle BCD</math> are perpendicular. | \item Prove that the tangents at <math>C</math> to the circumcircles of <math>\triangle ACD</math> and <math>\triangle BCD</math> are perpendicular. | ||
\end{enumerate} | \end{enumerate} | ||
Revision as of 11:36, 21 November 2017
Let 
be a point inside acute triangle 
such that 
and 
.
\renewcommand{\labelenumi}{\alph{enumi}.}
\begin{enumerate}
\item Calculate the ratio 
\item Prove that the tangents at 
to the circumcircles of 
and 
are perpendicular.
\end{enumerate}
