Triangles - Math Olympiad Problems

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As shown in the figure, circles O and P have radii 3 and 6, and are externally tangent. Points A and B are on the circle O, and points C and D are on the circle P. AD and BC are common
external tangents to both circles. Find the area of trapezoid AOPD.

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As shown in the figure, in triangle ABC, median BD intersects CF at E such that BF = 4 and BE = ED. Find the length of BA.

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In the accompanying figure, segments AB and CD are parallel, the measure of angle D is twice that of angle B, and the measures of segments AD and CD are a and b respectively. Then the measure of AB is equal to