- Is there is a convex quadrilateral which the diagonals divide into four triangles with areas of distinct primes?
- Is there a triangle with
area and cm perimeter? - Let
be the centroid of triangle , and the symmetric of wrt . Show that , , , are concyclic if and only if . - Three equal circles have a common point
and intersect in pairs at points , , . Prove that that is the orthocenter of triangle . - Let
be an isosceles triangle with . A semi-circle of diameter with , is tangent to the sides , in , respectively and intersects the semicircle at . Prove that passes through the midpoint of . - Parallels to the sides of a triangle passing through an interior point divide the inside of a triangle into
parts with the marked areas as in the figure. Show that - Let
, , be the midpoints of the arcs , , on the circumcircle of a triangle not containing the points , , , respectively. Let the line meets and at and , and let be the midpoint of the segment . Let the line meet and at and , and let be the midpoint of the segment .
a) Find the angles of triangle ;
b) Prove that if is the point of intersection of the lines and , then the circumcenter of triangle lies on the circumcircle of triangle .
Translate Whole Page to Read and Solve
Πέμπτη 30 Ιανουαρίου 2025
Junior Balkan Mathematical Olympiad 2003 [Shortlists & Solutions]
Εγγραφή σε:
Σχόλια ανάρτησης (Atom)