In the adjoining figure, if AD is the bisector of ∠A, what is AC?

1.	In the adjoining figure, if AD is the bisector of ∠A, what is AC?
Answer» Given AD is the bisector of ∠A in ΔABC. Let AC be x cm. We know that the angle bisector theorem states that the internal bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle. ⇒ \(\frac{AB}{AC}\) = \(\frac{DB}{DC}\) ⇒ \(\frac{6}{x}\) = \(\frac{3}{2}\) ⇒ x = \(\frac{6(2)}{3}\) ⇒ x = 4 cm ∴ AC = 4 cm

Answer»

Given AD is the bisector of ∠A in ΔABC. Let AC be x cm.

We know that the angle bisector theorem states that the internal bisector of an angle of a triangle divides the opposite side in two segments that are proportional to the other two sides of the triangle.

⇒ \(\frac{AB}{AC}\) = \(\frac{DB}{DC}\)

⇒ \(\frac{6}{x}\) = \(\frac{3}{2}\)

⇒ x = \(\frac{6(2)}{3}\)

⇒ x = 4 cm

∴ AC = 4 cm

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In the adjoining figure, if AD is the bisector of ∠A, what is AC?

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