MCQ
If P is any point within a $\triangle ABC$, then $\overline{ PA }+\overline{ CP }=$
- A$\overline{ AC }+\overline{ CB }$
- B$\overline{ BC }+\overline{ BA }$
- C$\overline{ CB }+\overline{ AB }$
- ✓$\overline{ CB }+\overline{ BA }$
✓
Answer
Correct option: D.
$\overline{ CB }+\overline{ BA }$
(D)
In $\triangle APC , \overline{ PA }+\overline{ AC }+\overline{ CP }=\overline{0}$ ...(i) …[Using triangle law of addition]
In $\triangle ABC , \overline{ AB }+\overline{ BC }=\overline{ AC }$ ...(ii)
From (i) and (ii), we get
$\begin{array}{l}\overline{ PA }+\overline{ CP }+\overline{ AB }+\overline{ BC }=\overline{0} \\ \Rightarrow \overline{ PA }+\overline{ CP }=\overline{ BA }+\overline{ CB }\end{array}$
In $\triangle APC , \overline{ PA }+\overline{ AC }+\overline{ CP }=\overline{0}$ ...(i) …[Using triangle law of addition]
In $\triangle ABC , \overline{ AB }+\overline{ BC }=\overline{ AC }$ ...(ii)
From (i) and (ii), we get
$\begin{array}{l}\overline{ PA }+\overline{ CP }+\overline{ AB }+\overline{ BC }=\overline{0} \\ \Rightarrow \overline{ PA }+\overline{ CP }=\overline{ BA }+\overline{ CB }\end{array}$
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