A high school compulsory 4 vector problem Given that the area of triangle ABC is 100, points D and E are the points on edge AB and BC respectively, and ad: DB = Ce: EB = 2:1, AE and CD intersect at point P, the area of triangle APC is calculated? It's best to use vector computation

A high school compulsory 4 vector problem Given that the area of triangle ABC is 100, points D and E are the points on edge AB and BC respectively, and ad: DB = Ce: EB = 2:1, AE and CD intersect at point P, the area of triangle APC is calculated? It's best to use vector computation

AD:DB=2:1
Triangle ADC area: Triangle BCD = 2:1
Triangle ADC area = 200 / 3, triangle BCD area = 100 / 3
CE:EB=2:1
Area of triangle AEC: BAE = 2:1
Triangle AEC area = 200 / 3, triangle Abe area = 100 / 3
Triangle AEC = triangle ADC, triangle ADP = triangle EPC
And triangle PEB = 0.5 * triangle PEC, triangle EPB = 0.5 * triangle APD
Triangle Abe = 2 * triangle APD. So triangle APD = 100 / 6
Triangle APC = 200 / 3-100 / 6 = 50