MathLabs

Problem 1

Let P be a point in the interior of triangle ABC. Let D, E, F be the intersections of AP with BC, BP with CA, and CP with AB, respectively. Prove that the area of triangle ABC is 6 if each of triangles PFA, PDB, and PEC has area 1.
Step 5 of 5: Add the three parts
Previous stepNext step
[ABC]=[PAB]+[PBC]+[PCA]=x+y+z=2+2+2=6.[ABC]=[PAB]+[PBC]+[PCA]=x+y+z=2+2+2=6.
Detailed analysis

The three triangles with common vertex P partition ABC, so their areas add to 6.