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13

Part of 1999 National Olympiad First Round

Problems(1)

Turkish NMO First Round - 1999 P-13 (Geometry)

Source:

7/3/2012
Square BDEC BDEC with center F F is constructed to the out of triangle ABC ABC 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 ∣BG∣ \left|BG\right| 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}
geometryangle bisector