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705-805 (Hard)|   Geometry|      
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Three circles are drawn within triangle ABC such that no two circles 08 Mar 2018, 21:20
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Difficulty:

75% (hard)

Question Stats:

39% (01:31) correct 61% (01:34) wrong based on 131 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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E
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Three circles are drawn within triangle ABC such that no two circles 08 Mar 2018, 21:22
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Bunuel
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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23. Geometry




24. Coordinate Geometry




25. Triangles




26. Polygons




27. Circles




28. Rectangular Solids and Cylinders




29. Graphs and Illustrations



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Three circles are drawn within triangle ABC such that no two circles 09 Mar 2018, 00:56
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Bunuel
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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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

hence, Answer: Option E

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
Screen Shot 2018-03-09 at 1.25.50 PM.png [ 198.75 KiB | Viewed 3932 times ]

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Three circles are drawn within triangle ABC such that no two circles 31 Mar 2021, 15:27
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