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

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

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New post 08 Mar 2018, 20:20
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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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New post 08 Mar 2018, 20:22
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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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

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New post 08 Mar 2018, 23:56
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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

hence, Answer: Option E

The discrepancy in figure is as depicted in the attachment.
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Re: Three circles are drawn within triangle ABC such that no two circles &nbs [#permalink] 08 Mar 2018, 23:56
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