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

Answer 1

To find the ratio ML : LC in triangle ABC with points M and N on sides AB and BC, respectively, we can use similar triangles and set up ratios based on the proportionality of corresponding sides. The ratio ML : LC is 3 : 5.

Step-by-step explanation:

Let ABC be a triangle with points M and N on sides AB and BC, respectively. Given that AM : MB = 1 : 2 and BN : NC = 2 : 3, we need to find the ratio of ML to LC.

Using similar triangles, we can set up ratios based on the proportionality of corresponding sides. Since triangles ANL and CML are similar, we have:

AN : CM = NL : ML

We can substitute the given ratios:

(AN + NL) : (CM + ML) = 3 : 5

Simplifying and solving for the ratio ML : LC:

5ML = 3LC

ML : LC = 3 : 5