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# Three circles are drawn within triangle ABC such that no two circles

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Math Expert
Joined: 02 Sep 2009
Posts: 56300
Three circles are drawn within triangle ABC such that no two circles  [#permalink]

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08 Mar 2018, 21:20
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Difficulty:

65% (hard)

Question Stats:

41% (01:34) correct 59% (01:26) wrong based on 53 sessions

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Three circles are drawn within triangle ABC such that no two circles overlap and that each is tangent to one another and to the triangle in at least one place. What is their combined area?

(1) The radius of one of the circles is 4.

(2) Triangle ABC is equilateral.

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Re: Three circles are drawn within triangle ABC such that no two circles  [#permalink]

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08 Mar 2018, 21:22
Bunuel wrote:
Three circles are drawn within triangle ABC such that no two circles overlap and that each is tangent to one another and to the triangle in at least one place. What is their combined area?

(1) The radius of one of the circles is 4.

(2) Triangle ABC is equilateral.

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Re: Three circles are drawn within triangle ABC such that no two circles  [#permalink]

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09 Mar 2018, 00:56
1
Bunuel wrote:
Three circles are drawn within triangle ABC such that no two circles overlap and that each is tangent to one another and to the triangle in at least one place. What is their combined area?

(1) The radius of one of the circles is 4.

(2) Triangle ABC is equilateral.

Even if we combine the statements

- We have no dimensional constraint to draw to equilateral triangle of any specific size
-Radius of other two circles is unknown which may vary
- The point of tangencies is minimum one which doesn't restrict the movement of circles within the triangle and doesn't limit the size of other two circles

The discrepancy in figure is as depicted in the attachment.
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Screen Shot 2018-03-09 at 1.25.50 PM.png [ 198.75 KiB | Viewed 450 times ]

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Re: Three circles are drawn within triangle ABC such that no two circles   [#permalink] 09 Mar 2018, 00:56
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