   Chapter 3.R, Problem 43E

Chapter
Section
Textbook Problem

# In Δ A B C , D lies on A B , C D ⊥ A B , | A D | = | B D | = 4  cm, and | C D | = 5  cm . Where should a point P be chosen on CD so that the sum | P A | + | P B | + | P C | is a minimum?

To determine

To find:

The point P such that the sum PA+PB+PC is minimum.

Explanation

1) Concept:

Find the absolute minimum in the given interval to get the minimum sum.

2) Formula:

i. The Pythagoras theorem states hypotenuse2=one side2+another side 2

ii. Power rule for xn is given by

ddxxn=nxn-1

iii.

ddxf(x)=12f(x)f'(x)

3) Given:

4) Calculation:

Draw ABC from the given condition

From the figure, we observe that ADP and BDP  are right angled triangles, so by Pythagoras theorem, AP=x2+16 and PB=x2+16  and CP=(5-x)

So that the sum is

PA+PB+PC<

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