Question

Let ABC be a triangle and pick points M and N on its sides AB and CB correspondingly so that AM : MB = 1 : 2 and BN : NC = 2 : 3 . Let AN intersect MC at point L. Find ML : LC . Use similar triangles to find ML: LC

Answer 1

To find ML:LC, we can use similar triangles. Let's start by finding the lengths of AM, MB, BN, and NC. If AM:MB = 1:2, and BN:NC = 2:3, then we can assign values to these lengths. Using the properties of similar triangles, we can find ML:LC by applying the ratio of corresponding sides.

Step-by-step explanation:

To find ML:LC, we can use similar triangles. Let's start by finding the lengths of AM, MB, BN, and NC. If AM:MB = 1:2, and BN:NC = 2:3, then we can assign values to these lengths. Let's say AM = 1, MB = 2, BN = 2, and NC = 3. Now, we can use the properties of similar triangles to find ML:LC. Since △ANL and △CMN are similar, we can apply the ratio of corresponding sides to find ML:LC.

Since AM:MB = 1:2, we can say that AN:NB = 1:3. Similarly, since BN:NC = 2:3, we can say that MC:CN = 1:2. Therefore, we have AN:NB:MC = 1:3:1 and ML:LC = AN:NB:MC = 1:3:1. So, ML:LC equals 1:3:1.