• Choice E

    A circle centered at OO has radius 1010 ft. A point is outside the circle if its distance from OO exceeds 1010.

    Use the Pythagorean theorem to find each point's distance from OO (each point is the hypotenuse vertex of a right triangle with legs as labeled):

    • AA: 42+92=16+81=979.85\sqrt{4^2 + 9^2} = \sqrt{16 + 81} = \sqrt{97} \approx 9.85 (inside)

    • BB: 62+82=36+64=100=10\sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10 (on the circle)

    • CC: 72+72=49+49=989.90\sqrt{7^2 + 7^2} = \sqrt{49 + 49} = \sqrt{98} \approx 9.90 (inside)

    • DD: 62+102=36+100=13611.66\sqrt{6^2 + 10^2} = \sqrt{36 + 100} = \sqrt{136} \approx 11.66 (outside)

    • EE: 12+102=1+100=10110.05\sqrt{1^2 + 10^2} = \sqrt{1 + 100} = \sqrt{101} \approx 10.05 (outside)

    Point EE with legs 11 and 1010 has distance 101>10\sqrt{101} > 10, so it is outside the circle.

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