jay_shark
02-22-2007, 06:16 PM
Here is a question I thought of which I haven't seen before or maybe I have but don't remember .
Take any triangle A,B,C and three lines emanating from each vertex to the opposite side of the triangle so the three lines meet at a common point . Call these points A',B',C' opposite of A,B,C . There will be 4 triangles with the middle triangle being A'B'C' . Show that the sum of the areas of the three outer triangles is greater than or equal to three times the area of the middle triangle . Equality occurs when the three lines meet at the centroid of the triangle .
Do you believe this to be true ?
Take any triangle A,B,C and three lines emanating from each vertex to the opposite side of the triangle so the three lines meet at a common point . Call these points A',B',C' opposite of A,B,C . There will be 4 triangles with the middle triangle being A'B'C' . Show that the sum of the areas of the three outer triangles is greater than or equal to three times the area of the middle triangle . Equality occurs when the three lines meet at the centroid of the triangle .
Do you believe this to be true ?