# A line parallel to side AC of triangle ABC intersects sides AB and BC at points K and M, respectively. Find AC if BK: KA = 1: 4, KM = 13.

May 31, 2020 | Education

| Consider the triangles ABC and KBM.

∠B is common.

∠BAC = ∠BKM (since these are the corresponding angles)

∠BCA = ∠BMK (since these are also the corresponding angles)

Therefore, these triangles are similar in the first sign of similarity.

Then by the definition of such triangles:

BA / BK = AC / KM

(BK + KA) / BK = AC / KM

1 + KA / BK = AC / KM

1 + 4/1 = AC / KM

5 = AC / 13

AC = 5 * 13 = 65

Answer: AC = 65

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