Turkish NMO First Round - 1999 P-13 (Geometry)
Source:
July 3, 2012
geometryangle bisector
Problem Statement
Square with center is constructed to the out of triangle such that \angle A \equal{} 90{}^\circ, \left|AB\right| \equal{} \sqrt {12}, \left|AC\right| \equal{} 2. If \left[AF\right]\bigcap \left[BC\right] \equal{} \left\{G\right\} , then will be(A)\ 6 \minus{} 2\sqrt {3} \qquad(B)\ 2\sqrt {3} \minus{} 1 \qquad(C)\ 2 \plus{} \sqrt {3} \\ \qquad(D)\ 4 \minus{} \sqrt {3} \qquad(E)\ 5 \minus{} 2\sqrt {2}