This figure shows △ABC . BD⎯⎯⎯⎯⎯ is the angle bisector of ∠ABC . What is AD ? Enter your answer, as a fraction, in the box. units

This figure shows △ABC . BD⎯⎯⎯⎯⎯ is the angle bisector of ∠ABC .

What is AD ?

Enter your answer, as a fraction, in the box.

units

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1 Answer
Jan 20, 2018

#color(green)(AD = 8/3)#

Explanation:

In geometry, the angle bisector theorem is concerned with the relative lengths of the two segments that a triangle's side is divided into by a line that bisects the opposite angle. It equates their relative lengths to the relative lengths of the other two sides of the triangle.

From the above diagram,

#(AB) / (BC) = (AD) / (DC) #as per the angle bisector theorem.

Given #AB = 6, BC = 10, AD + DC = AC = 6#

#:. DC = AC - AD = 6 - AD#

Hence, #8 / 10 = (AD) / (6 - AD)#

#48 - 8 (AD) = 10 (AD)#

#AD = 48 / 18 = color (green)(8/3)#