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2025 AMC 10B Problem 13

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2025 AMC 10B Problem 13AMC 10 Step by Step
Name:                             Date: September 13, 2026
Triangle Centers & Cevians · difficulty 3 of 5 · about 5 min · position P11-15

The altitude to the hypotenuse of a 30−60−90∘30{-}60{-}90^\circ right triangle is divided into two segments of lengths x<yx < y by the median to the shortest side of the triangle. What is the ratio xx+y\tfrac{x}{x+y} ?

  1. A)

    37\frac 37

  2. B)

    34\frac{\sqrt3}{4}

  3. C)

    49\frac 49

  4. D)

    511\frac{5}{11}

  5. E)

    4315\frac{4\sqrt3}{15}

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