# Difference between revisions of "2005 AMC 10A Problems/Problem 23"

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− | BCDE is a square. Point A is chosen outside of BCDE such that angle BAC= 120 and AB=AC. Point F is chosen inside BCDE such that the | + | ==Problem== |

+ | <math>BCDE</math> is a [[square (geometry) | square]]. [[Point]] <math>A</math> is chosen outside of <math>BCDE</math> such that [[angle]] <math>BAC= 120^\circ</math> and <math>AB=AC</math>. Point <math>F</math> is chosen inside <math>BCDE</math> such that the [[triangle]]s <math>ABC</math> and <math>FCD</math> are [[congruent (geometry) | congruent]]. If <math>AF=20</math>, compute the [[area]] of <math>BCDE</math>. | ||

(A)1/6 (B) 1/4 (C) 1/3 (D) 1/2 (E)2/3 | (A)1/6 (B) 1/4 (C) 1/3 (D) 1/2 (E)2/3 | ||

+ | |||

+ | <math> \mathrm{(A) \ } \frac{1}{6}\qquad \mathrm{(B) \ } \frac{1}{4}\qquad \mathrm{(C) \ } \frac{1}{3}\qquad \mathrm{(D) \ } \frac{1}{2}\qquad \mathrm{(E) \ } \frac{2}{3} </math> | ||

+ | |||

+ | ==Solution== | ||

+ | {{solution}} | ||

+ | |||

+ | ==See also== | ||

+ | |||

+ | |||

+ | [[Category:Introductory Geometry Problems]] |

## Revision as of 13:43, 14 February 2007

## Problem

is a square. Point is chosen outside of such that angle and . Point is chosen inside such that the triangles and are congruent. If , compute the area of .

(A)1/6 (B) 1/4 (C) 1/3 (D) 1/2 (E)2/3

## Solution

*This problem needs a solution. If you have a solution for it, please help us out by adding it.*