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?

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

    posted by Steve

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