MathDB

2012.D2

Part of Durer Math Competition CD 1st Round - geometry

Problems(1)

sum of gray ares is half of the triangles' area 2011-12 Durer Round1 D2

Source:

12/3/2022
Durer drew a regular triangle and then poked at an interior point. He made perpendiculars from it sides and connected it to the vertices. In this way, 66 small triangles were created, of which (moving clockwise) all the second one is painted gray, as shown in figure. Show that the sum of the gray areas is just half the area of the triangle. https://cdn.artofproblemsolving.com/attachments/e/7/a84ad28b3cd45bd0ce455cee2446222fd3eac2.png
geometryareasDurer