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Bunuel
A, B, C and D are points on a line, with D the midpoint of segment BC. The lengths of segments AB, AC and BC are 10, 2, 12, respectively. What is the length of segment AD?

(A) 2
(B) 4
(C) 6
(D) 10
(E) 12
Try to find endpoints first. D cannot be one; it's a midpoint.

Consider that BC at 12 has the greatest length. AC and AB sum to BC. Therefore, like D, A is between B and C. They must be the endpoints, with D halfway between, at D = 6.

Start with B, C , and D.

We have either

B_______6________D______6_______C ---------> OR

C_______6________D______6_______B

Now there's A, whose placement will yield which order above is correct. AC(CA) = 2. AB = 10. A is much closer to C, and CA + AB = CB(BC), which is 2 + 10 = 12. Correct. Order and values must be

C_______A___________D_________________B
0_______2___________6_________________12

D=6, A=2. AD = 4.

Answer B
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Since the longest length of the given line is 12 then the end points are B and C also since D is the midpoint of the line BD=DC , DC= DA+AC DC=6 , AC =2 and so AD= 6-2=4

Am i correct in my explanation?? Thank you
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