MathDB

33

Part of 1999 National Olympiad First Round

Problems(1)

Turkish NMO First Round - 1999 P-33 (Geometry)

Source:

7/3/2012
\left|AC\right| \equal{} 8 \sqrt {2}, B B is the midpoint of [AC] \left[AC\right], E E is the midpoint of arc AB AB of a circle having chord [AB] \left[AB\right], and D D is the point of tangency drawing from C C.(D D lies on the opposite side of line AB AB to E E). If \left[DE\right]\bigcap \left[AB\right] \equal{} \left\{F\right\}, \left|CF\right| \equal{} ?
<spanclass=′latex−bold′>(A)</span> 52<spanclass=′latex−bold′>(B)</span> 42<spanclass=′latex−bold′>(C)</span> 8<spanclass=′latex−bold′>(D)</span> 6<spanclass=′latex−bold′>(E)</span> 43<span class='latex-bold'>(A)</span>\ 5\sqrt {2} \qquad<span class='latex-bold'>(B)</span>\ 4\sqrt {2} \qquad<span class='latex-bold'>(C)</span>\ 8 \qquad<span class='latex-bold'>(D)</span>\ 6 \qquad<span class='latex-bold'>(E)</span>\ 4\sqrt {3}
geometry