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i dont understand this geometry solution

http://docs.google.com/Doc?id=dc83hzcs_269f55p6t

can you please clarify ?

2007-10-31 16:31:19 · 2 answers · asked by calculus 1 in Science & Mathematics Mathematics

2 answers

Doubt 1: The theorem used is the angle bisector theorem. In your case, BD/DC = AB/AC. Google "angle bisector theorem wiki" for details.

Doubt 2: They're saying that if angle A is 90 degrees, they just proved that BD is less than 2.15. Therefore, if angle A is less than 90, BD will be even smaller, so angle A must be greater than 90 degrees. Choice 4 is the only one that's possible.

2007-10-31 18:09:04 · answer #1 · answered by Anonymous · 0 0

The first doubt can be clarified if you use the sine rule.
Let angle ADB = θ and ADC = 180 - θ
BAD = DAC = 45

So BD / sin45 = 3/sinθ
Also (5-BD)/sin45 = 4/sin(180 - θ) = 4/sinθ
So BD / (5 - BD) = 3/4
4BD = 15 - 3BD
7BD = 15
BD = 15/7

In the case where angle A > 90, side BC = x > 5
so the above equation becomes
BD / (x - BD) = 3/4
BD = 3x / 7
So if x > 5, BD > 15/7

2007-10-31 17:07:08 · answer #2 · answered by Dr D 7 · 0 0

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