Difference between revisions of "1992 IMO Problems/Problem 4"
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In the plane let <math>C</math> be a circle, <math>l</math> a line tangent to the circle <math>C</math>, and <math>M</math> a point on <math>l</math>. Find the locus of all points <math>P</math> with the following property: there exists two points <math>Q</math>, <math>R</math> on <math>l</math> such that <math>M</math> is the midpoint of <math>QR</math> and <math>C</math> is the inscribed circle of triangle <math>PQR</math>. | In the plane let <math>C</math> be a circle, <math>l</math> a line tangent to the circle <math>C</math>, and <math>M</math> a point on <math>l</math>. Find the locus of all points <math>P</math> with the following property: there exists two points <math>Q</math>, <math>R</math> on <math>l</math> such that <math>M</math> is the midpoint of <math>QR</math> and <math>C</math> is the inscribed circle of triangle <math>PQR</math>. | ||
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| + | ==Video Solution== | ||
| + | https://www.youtube.com/watch?v=ObCzaZwujGw | ||
==Solution== | ==Solution== | ||
{{solution}} | {{solution}} | ||
Revision as of 16:43, 12 November 2023
Problem
In the plane let 
be a circle, 
a line tangent to the circle , and 
a point on . Find the locus of all points 
with the following property: there exists two points 
, 
on such that is the midpoint of 
and is the inscribed circle of triangle 
.
Video Solution
https://www.youtube.com/watch?v=ObCzaZwujGw
Solution
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