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Question

If P is any point within a ABC, then PA+CP is equal to?


A

AC+CB

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B

BC+BA

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C

CB+AB

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D

CB+BA

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Solution

The correct option is D

CB+BA


Explanation for the correct options:

Step 1: Draw a required triangle

ABC shown in the figure

Here, P is the mid point or center of the triangle and AB,BA,andCA are the sides of the triangle.

The triangle property states that the third side of a triangle is always equal to the sum of the lengths of any two of its sides.

Therefore,CP+PA=CA....(1)

CA=CB+BA [By Triangle Laws]

Step 2: Substituting the value of CA in equation (1) we get,

CP+PA=CB+BAPA+CP=CB+BA

Hence, the correct answer is an option (D)


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