Question

in the diagram below points A and B are 3 inches apart try to find two points that are 1 inch from point A and 1.5 inches from B why do you think it is impossible to find such points

Answer 1

Given :  points A and B are 3 inches apart  

To find : points that are 1 inch from point A and 1.5 inches from B

Solution:

A and B are 3 inches apart

=> AB =  3 inch

points 1 inch from point A and 1.5 inches from B

Let say Point is C

would Either be colinear  or form a Triangle with Ab

Case 1 : colinear

AC  = 1 inch

BC = 1.5nch

AB = 3 inch

As per segment addition postulate

1 + 1.5 inch  should equal to 3 inch

Hence colinear point is not possible

Case 2 :  Form a triangle

AC  = 1 inch

BC = 1.5nch

AB = 3 inch

in triangle sum of any two sides > third side

but 1 + 1.5  = 2.5 inch  < 3 inch

Hence triangle is not possible

Hence such point can not exist.

so impossible to find such points

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