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Let AB is divided internally and externally at P and Q in the same ratio. Then AP, AB, AQ are in AP or GP or HP??? Explain pls.

Let AB is divided internally and externally at P and Q in the same ratio. Then  AP, AB, AQ are in AP or GP or HP??? Explain pls.

Grade:12th Pass

1 Answers

Abhishek Patil
16 Points
9 years ago

 

AB is a line and P and Q divide in same ratio. Therefore,

1). Internally

Let AP = x then,

AQ = 2x and AB = 3x.

Thus AP, AQ and AB are in GP and AP(since x, 2x and 3x are in GP and AP).

2). Externally

Let AB = x then,

AP = 2x and AQ = 3x.

Thus AB, AP and AQ are in GP and AP(since x, 2x and 3x are in GP and AP).

Therefore they will be in AP and GP.

 

 

Therefore, we can say that

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