In a triangle ABC, the bisector of angle A cuts BC at D. If AB+AC=10 cm and BD:DC=3:1 then what is the length of AC?

Explanation

By the Angle Bisector Theorem, \frac{AB}{AC} = \frac{BD}{DC} = \frac{3}{1}. Thus, AB = 3AC. Substituting into AB+AC=10 gives 4AC = 10 \implies AC = 2.5 cm.

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