# 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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3. π 82
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 = β(5^2+13^2) = β194

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posted by Steve
2. I agree with your answers for the length of PA, AB, PR, BQ except for QP. to solve for QP you'll do the β(13^2-5^2)=12. Since PABQ is a trapezoid, AB will be one of its opposite sides which will also act as the hypotenuse of the right-angled triangle within

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posted by Joyce

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