P is a point in the interior of ∆ABC as shown in Fig. State which of the following statements are true (T) or false (F):

(i) AP + PB < AB
(ii) AP + PC > AC
(iii) BP + PC = BC

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Solution

(i) False
We know that the sum of any two sides of a triangle is greater than the third side; it is not true for the given triangle.

(ii) True
We know that the sum of any two sides of a triangle is greater than the third side; it is true for the given triangle.

(iii) False
We know that the sum of any two sides of a triangle is greater than the third side; it is not true for the given triangle.

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