Question

In a triangle ABC, E is the midpoint of BC and D is a point on AB such that AD : DB = 2 : 1. If CD and AE intersect at P, determine the ratio CP : PD.

Answer 1

Answer on Question #56335 – Math – Geometry

In a triangle ABC, E is the midpoint of BC and D is a point on AB such that AD : DB = 2 : 1. If CD and AE intersect at P, determine the ratio CP : PD.

Solution

Let’s consider the triangle $CDB$ which is cut by the line $AE$. According to Menelaus’ theorem:

$$\frac{BE}{EC} * \frac{CP}{PD} * \frac{DA}{AB} = 1$$

So

$$\frac{CP}{PD} = \frac{EC}{BE} * \frac{AB}{DA} = 1 * \frac{2x + x}{2x} = \frac{3}{2}$$

Answer: $\frac{3}{2}$.

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