MathDB

15

Part of 2006 JBMO ShortLists

Problems(1)

areas of triangles are distinct primes, area of quadr. an integer, min area

Source: JBMO Shortlist 2006 G6

7/23/2019
Let A1A_1 and B1B_1 be internal points lying on the sides BCBC and ACAC of the triangle ABCABC respectively and segments AA1AA_1 and BB1BB_1 meet at OO. The areas of the triangles AOB1,AOBAOB_1,AOB and BOA1BOA_1 are distinct prime numbers and the area of the quadrilateral A1OB1CA_1OB_1C is an integer. Find the least possible value of the area of the triangle ABCABC, and argue the existence of such a triangle.
geometryareasminimumprime numbersInteger