Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

1987 OIM Problems/Problem 2

Revision as of 11:47, 13 December 2023 by Tomasdiaz (talk | contribs) (Created page with "== 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> i...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

On a triangle $ABC$, $M$ and $N$ are the respective midpoints of sides $AC$ and $AB$, and $P$ is the midpoint of the intersection of $BM$ and $CN$. Prove that, if is possible to inscribe a circumference in the quadrilateral $ANPM$, then triangle $ABC$ is isosceles.

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=1987_OIM_Problems/Problem_2&oldid=206975"