Question

Points D, E and F are on the sides AB, BC and AC, respectively, of triangle ABC such that AE, BF and CD bisect ∠A, ∠B and ∠C, respectively. If AB = 6 cm, BC = 7 cm and AC = 8 cm, then what will be the length of BE?

• A. 3.5 cm
• B. 3.6 cm
• C. 4 cm
• D. 3 cm

Answer 1

Answer:

D. 3 cm

Given AB = 6 cm, BC = 7 cm and AC = 8 cm Concept Internal angle bisector theorem The internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle. In ∆ABC, AE bisects ∠A. (BE/EC) = (AB/AC) BE/(7 - BE) = 6/8 8 BE = 42 - 6BE 14 BE = 42 BE = 42/14 BE = 3 cm ∴ The length of BE is 3 cm.