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Pints A,B,C lie on a circle with radius 1. What is the area

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Pints A,B,C lie on a circle with radius 1. What is the area [#permalink] New post 24 Jul 2007, 12:01
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Pints A,B,C lie on a circle with radius 1. What is the area of triangle ABC?

AB^2=BC^2+AC^2

angle CAB = 30 degrees











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I understand that both statements together give us that it is a 30-60-90 right triangle, and I know the ratios of the sides of a 30-60-90; but I couldn't figure out how to derive the area. If a 30-60-90 triangle is incribed in a circle, does that automatically mean one of the sides of the triangle is the diameter of the circle? is this true for any 90 degree triangle inscribed in a circle?
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 [#permalink] New post 24 Jul 2007, 12:07
does that automatically mean one of the sides of the triangle is the diameter of the circle?

Yes. The area should be root of 3 over 8.
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 [#permalink] New post 24 Jul 2007, 13:03
Hayabusa wrote:
dahcrap wrote:
I get A.


Could you explain that?

I get C.


Oops am sorry I was just too quick in my answer. It has to be C
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 [#permalink] New post 24 Jul 2007, 13:19
So, does this say that any right triangle inscribed in a circle has one side equal to the length of the diameter?...or just for a 30-60-90 right triangle?
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 [#permalink] New post 24 Jul 2007, 13:56
Hayabusa wrote:
zakk wrote:
Hayabusa wrote:
emoryhopeful wrote:
So, does this say that any right triangle inscribed in a circle has one side equal to the length of the diameter?...or just for a 30-60-90 right triangle?



Yes.


hmmm...Yes to both?


Oooops. Yes to the first one only.


OK, now I think I get it. 1 isn't sufficent becasue we don't have any values, so we're to BCE.

Now I see why 2 works, based on the rule your gave.

Is this correct?
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 [#permalink] New post 24 Jul 2007, 14:08
zakk wrote:
Hayabusa wrote:
zakk wrote:
Hayabusa wrote:
emoryhopeful wrote:
So, does this say that any right triangle inscribed in a circle has one side equal to the length of the diameter?...or just for a 30-60-90 right triangle?



Yes.


hmmm...Yes to both?


Oooops. Yes to the first one only.


OK, now I think I get it. 1 isn't sufficent becasue we don't have any values, so we're to BCE.

Now I see why 2 works, based on the rule your gave.

Is this correct?



From 1, we know that it is a right triangle with a hypotenuse of 2. Can't get the area - Insuff.

From 2 we know that an angle is 30 deg - Insuff

Both - we know that we have a right triangle, know the hypotenuse and know that it is 2-1-root of 3. Area should be root of 3 over 2.
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 [#permalink] New post 24 Jul 2007, 14:12
OK. I need to review the OG geometry section :)

I'm grasping the idea, just need to get the formula in my head. thanks for the explanation.
  [#permalink] 24 Jul 2007, 14:12
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