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2000 AMC 10 Problem 16

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2000 AMC 10 Problem 16AMC 10 Step by Step
Name:                             Date: September 13, 2026
Coordinate Geometry · difficulty 3 of 5 · about 5 min · position P16-20

The diagram shows 2828 lattice points, each one unit from its nearest neighbors. Segment ABAB meets segment CDCD at EE . Find the length of segment AEAE .

figure

  1. A)

    453\frac{4\sqrt{5}}{3}

  2. B)

    553\frac{5\sqrt{5}}{3}

  3. C)

    1257\frac{12\sqrt{5}}{7}

  4. D)

    252\sqrt{5}

  5. E)

    5659\frac{5\sqrt{65}}{9}

Working