Difference between revisions of "1987 OIM Problems/Problem 2"
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== Problem == | == Problem == | ||
On a triangle <math>ABC</math>, <math>M</math> and <math>N</math> are the respective midpoints of sides <math>AC</math> and <math>AB</math>, and <math>P</math> is the midpoint of the intersection of <math>BM</math> and <math>CN</math>. Prove that, if is possible to inscribe a circumference in the quadrilateral <math>ANPM</math>, then triangle <math>ABC</math> is isosceles. | On a triangle <math>ABC</math>, <math>M</math> and <math>N</math> are the respective midpoints of sides <math>AC</math> and <math>AB</math>, and <math>P</math> is the midpoint of the intersection of <math>BM</math> and <math>CN</math>. Prove that, if is possible to inscribe a circumference in the quadrilateral <math>ANPM</math>, then triangle <math>ABC</math> is isosceles. | ||
| + | |||
| + | ~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ||
== Solution == | == Solution == | ||
{{solution}} | {{solution}} | ||
| + | |||
| + | == See also == | ||
| + | https://www.oma.org.ar/enunciados/ibe2.htm | ||
Latest revision as of 12:26, 13 December 2023
Problem
On a triangle 
, 
and 
are the respective midpoints of sides 
and 
, and 
is the midpoint of the intersection of 
and 
. Prove that, if is possible to inscribe a circumference in the quadrilateral 
, then triangle is isosceles.
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
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