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# What is the area of a triangle (with vertices at FCE) that is inscribe

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18 Sep 2017, 13:12
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Difficulty:

75% (hard)

Question Stats:

32% (00:49) correct 68% (01:10) wrong based on 28 sessions

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What is the area of a triangle (with vertices at FCE) that is inscribed in a hexagon with vertices at ABCDE?

(1) The hexagon is regular and BE = 14.
(2) EC = 7$$\sqrt{3}$$.

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What is the area of a triangle (with vertices at FCE) that is inscribe  [#permalink]

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19 Sep 2017, 10:54
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What is the area of a triangle (with vertices at FCE) that is inscribed in a hexagon with vertices at ABCDE?

(1) The hexagon is regular and BE = 14.
(2) EC = 7$$\sqrt{3}$$.

In the hexagon, BE=14, which is diameter of circumscribed circle of a hexagon.
Hence FC=14 which is another diameter.
In triangle FCE, LFEC=90deg, because angle formed at the semi-circle is 90deg.
Then we can find side FE which is same as radius of the circle i.e. 7m.
Knowing FE and EC, we can find the area of triangle FCE.
Sufficient.

S2- EC=7$$\sqrt{3}$$
but we dont know any other dimensions, hence not sufficient.

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