Math

A circle with a 4-inch radius is centered at A, and a circle with a 9-inch radius is centered at B, where A and B are 13 inches apart. There is a segment that is tangent to the small circle at P and to the large circle at Q. It is a common external tangent of the two circles. What kind of quadrilateral is PABQ? What are the lengths of its sides?

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asked by Matty
  1. Draw the figure. Since AP and BQ are parallel, PABQ is a trapezoid.

    Draw PR to intersect BQ at R.

    AP=BR=4 so RQ=5

    So, the sides are
    PA=4
    AB=PR=13
    BQ=9
    QP = √(5^2+13^2) = √194

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    posted by Steve

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