Question

C, D are two interior points of line segment AB, such that C is a midpoint of AD, D is midpoint of CB, then express AD+CB in terms of AB.​

Answer 1

Given

• C is Mid-point of AD
• D is Mid-point of CB

To Express

• AD+CB in terms of AB.

_________Solution___________

C is Mid-point of AD

• AC = CD ______Equation(1)

D is Mid-point of CB

• DB = CD _____ Equation (2)

From Equation (1) and (2)

• AC = DB

Therefore, AC = CD = DB

Now,

$\\ →AC + DC + BD = AB$

$→AC + AC + AC = AB$

$→3AC = AB$

$→AC = AB/3$

Or,

$→CD = AB/3$

Or,

$→DB = AB/3$

According to Question

${AB + CB = AC + CD + CD + DB}$

${AB + CB = AB/3 ~~+~~ AB/3~~+~~AB/3~~+~~AB/3}$

${AB + CB = AB +AB +AB +AB /3 }$

${AB + CB = 4AB /3 }$

Answer 2

• Given
• C is Mid-point of AD
• D is Mid-point of CB
• To Express
• AD+CB in terms of AB.
• _________Solution___________
• C is Mid-point of AD
• AC = CD ______Equation(1)
• D is Mid-point of CB
• DB = CD _____ Equation (2)
• From Equation (1) and (2)
• AC = DB
• Therefore, AC = CD = DB
• Now,
• \begin{gathered} \\ →AC + DC + BD = AB \end{gathered}
• →AC+DC+BD=AB
• →AC + AC + AC = AB→AC+AC+AC=AB
• →3AC = AB→3AC=AB
• →AC = AB/3→AC=AB/3
• Or,
• →CD = AB/3→CD=AB/3
• Or,
• →DB = AB/3→DB=AB/3
• According to Question
• {AB + CB = AC + CD + CD + DB}AB+CB=AC+CD+CD+DB
• {AB + CB = AB/3 ~~+~~ AB/3~~+~~AB/3~~+~~AB/3}AB+CB=AB/3 + AB/3 + AB/3 + AB/3
• {AB + CB = AB +AB +AB +AB /3 }AB+CB=AB+AB+AB+AB/3
• {AB + CB = 4AB /3 }AB+CB=4AB/3