Question

?? explain this..




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Answer 1

please find the attachment

Answer 2

From basic proportionality theorem, you get the fourth part directly.

AD/AB = AE/AC
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Take its reciprocal. you will get third part.

AB/AD = AC/AE
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You know
AB = AD + DB
AC = AE + EC

Now subtract 1 from both sides of (iii), you will get (ii)

$\frac{ab}{ad} - 1 = \frac{ac}{ae} - 1 \\ \\ \frac{ab - ad}{ad} = \frac{ac - ae}{ae} \\ \\ \frac{db}{ad} = \frac{ec}{ae}$
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Take reciprocal of (ii), you will get (i)

AD/DB = AE/EC
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Now add 1 to both sides of (i), you will get (v)

$\frac{ad}{db} = \frac{ae}{ec} \\ \\ \frac{ad}{db} + 1 = \frac{ae}{ec} + 1 \\ \\ \frac{ad + db}{db} = \frac{ae + ec}{ec} \\ \\ \frac{ab}{db} = \frac{ac}{ec}$
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Take reciprocal of (v), you will get (vi)

DB/AB = EC/AC

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From the 6 given, Actually there are 3 results. You can get the other 3 just by taking reciprocal.

I and ii are reciprocal of each other
iii and iv are reciprocal of each other
v and vi are reciprocal of each other
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IV is the direct result from theorem.

You can get the rest two by taking reciprocal and subtracting or adding 1. you have to see what you need to do. Whether you need to take reciprocal or not, whether to subtract or add 1.