Difference between revisions of "2002 OIM Problems/Problem 4"
(Created page with "== Problem == Let <math>M = {1, 2, \cdots , 49}</math> be the set of the first <math>49</math> positive integers. Determine the maximum integer <math>k</math> such that the se...") |
|||
| Line 1: | Line 1: | ||
== Problem == | == Problem == | ||
| − | + | In a scalene triangle <math>ABC</math>, the interior bisector <math>BD</math> is drawn, with <math>D</math> on <math>AC</math>. Let <math>E</math> and <math>F</math>, respectively, be the feet of the perpendiculars drawn from <math>A</math> and <math>C</math> towards the line | |
| + | <math>BD</math>, and let <math>M</math> be the point on side <math>BC</math> such that <math>DM</math> is perpendicular to <math>BC</math>. Show that | ||
| + | <math>\angle EMD = \angle DMF</math>. | ||
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ||
Revision as of 03:43, 14 December 2023
Problem
In a scalene triangle 
, the interior bisector 
is drawn, with 
on 
. Let 
and 
, respectively, be the feet of the perpendiculars drawn from 
and 
towards the line
, and let 
be the point on side 
such that 
is perpendicular to . Show that
.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
