   Chapter 5.6, Problem 37E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In right Δ A D C , D C = 5 and A C = 5 3 . If A D → bisects ∠ B A C , find B D . To determine

To find:

BD.

Explanation

Given:

In a right ΔABC with right C, AD bisects BAC and DC=5,AC=53.

Theorem used:

Angle bisector theorem:

If a ray bisects one angle of a triangle, then it divides the opposite side into segments whose lengths are proportional to the lengths of the two sides that form the bisected angle.

Calculation:

Consider a right ΔABC.

Given that AD bisects BAC.

By angle bisector theorem, we get

ABAC=BDDC

ACDC=ABBD

We have DC=5,AC=53.

535=ABBD31=ABBD

AB:BD=3:1

Let AB=3x,BD=x

From the figure we see that, BC=BD+DC

BC=x+5

Consider the right triangle ABC with right angle at C

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