Difference between revisions of "1992 OIM Problems/Problem 3"
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~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ~translated into English by Tomas Diaz. ~orders@tomasdiaz.com | ||
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== Solution == | == Solution == | ||
+ | * Note. I actually competed at this event in Venezuela when I was in High School representing Puerto Rico. I got full points for part a and partial points for part b. I don't remember what I did. I will try to write a solution for this one later. | ||
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{{solution}} | {{solution}} | ||
== See also == | == See also == | ||
https://www.oma.org.ar/enunciados/ibe7.htm | https://www.oma.org.ar/enunciados/ibe7.htm |
Revision as of 18:20, 14 December 2023
Problem
In an equilateral triangle whose side has length 2, the circle
is inscribed.
a. Show that for every point of
, the sum of the squares of its distances to the vertices
,
and
is 5.
b. Show that for every point in
it is possible to construct a triangle whose sides have the lengths of the segments
,
and
, and that its area is:
~translated into English by Tomas Diaz. ~orders@tomasdiaz.com
Solution
- Note. I actually competed at this event in Venezuela when I was in High School representing Puerto Rico. I got full points for part a and partial points for part b. I don't remember what I did. I will try to write a solution for this one later.
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