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# What is the radius of the circle with center A ?

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What is the radius of the circle with center A ? [#permalink]  19 Jun 2014, 03:35
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What is the radius of the circle with center A ?

(1) BC = $$2\sqrt{3}$$

(2) Angle BCA has a measure of 30°
[Reveal] Spoiler: OA

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Re: What is the radius of the circle with center A ? [#permalink]  19 Jun 2014, 03:58
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What is the radius of the circle with center A ?

(1) BC = $$2\sqrt{3}$$. We have the length of a chord, which is clearly insufficient to answer the question. Not sufficient.

(2) Angle BCA has a measure of 30°. Notice that since AB = AC = radius, then triangle ABC is isosceles, which means that angles at B and C are equal. So, we have that angle B = angle C = 30° and angle A = 180 - (30 + 30) = 120°. We know all the angles in ABC but we don't know any of the lengths. Not sufficient.

(1)+(2) We know all the angles in ABC and the length of one of the sides, BC. So, we can find any other length there, including AC (radius). Sufficient.

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Re: What is the radius of the circle with center A ? [#permalink]  19 Jun 2014, 06:39
Hi Bunuel, How can we find out the length of other two sides of a triangle(isosceles) by knowing all the angles and length of one side?
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Re: What is the radius of the circle with center A ? [#permalink]  19 Jun 2014, 07:29
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varikaur wrote:
Hi Bunuel, How can we find out the length of other two sides of a triangle(isosceles) by knowing all the angles and length of one side?

We don't really need to find the actual value, knowing that we can find is enough for DS questions.

But if still interested, below diagram should give you a hint:
Attachment:

Untitled.png [ 74.31 KiB | Viewed 449 times ]

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Re: What is the radius of the circle with center A ?   [#permalink] 19 Jun 2014, 07:29
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