In triangle ABC, point D divides side so that AD:DC=1:2. Let E be the midpoint of and let F be the point of intersection of line BC and line AE. Given that the area of ABC is 360, what is the area of EBF?

AMC 8 2019 Problem 24

AMC8 2019 年第 24 题

三角形★★★★★

In triangle ABC, point D divides side \overlineAC so that AD:DC=1:2. Let E be the midpoint of \overlineBD and let F be the point of intersection of line BC and line AE. Given that the area of \triangle ABC is 360, what is the area of \triangle EBF?

在三角形 ABC 中，点 D 把边分成的两段满足 AD:DC＝1:2，点 E 是线段的中点，F 是直线 BC 和 AE 的交点。已知 ΔABC 的面积是 360，问 ΔEBF 的面积是多少？

A.24
B.30
C.32
D.36
E.40

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