MathDB

2008.1

Part of Swiss NMO - geometry

Problems(1)

a square has equal area with a triangle, 2 circumcenters related

Source: Switzerland - Swiss MO 2008 p1

7/17/2020
Let ABCABC be a triangle with ∠BAC≠45o\angle BAC \ne 45^o and ∠ABC≠135o\angle ABC \ne 135^o. Let PP be the point on the line ABAB with ∠CPB=45o\angle CPB = 45^o. Let O1O_1 and O2O_2 be the centers of the circumcircles of the triangles ACPACP and BCPBCP respectively. Show that the area of the square CO1PO2CO_1P O_2 is equal to the area of the triangle ABCABC.
geometrycircumcircleareasequal areas