SOLUTION: A, B,C, D are collinear. If BC = CD, BD = AB - 1, and AD = 9. Find AB, BC, CD and BD?

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Question 282505: A, B,C, D are collinear. If BC = CD, BD = AB - 1, and AD = 9. Find AB, BC, CD and BD?
Answer by solver91311(24713) About Me  (Show Source):
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Just so the explanation doesn't look quite so ugly with all of those capital letters that make you keep referring back to the diagram, I'm going to let represent the value of the measure of AB. Likewise, the value of the measure of BC will be and the value of the measure of CD will be CD. The value of the measure of AD is given as 9.

We are given that and we can see that AD is the sum of , so we can write:



Also, we are given that

which is to say:



Solving this little system we get





And knowing that

we can substitute



So AB = 5, BC = 4, and CD = 4, and BD must be 8.


John