MathDB

3

Part of 2023 Paraguay Mathematical Olympiad

Problems(1)

4 tangent circles with collinear centers OMAPA Paraguay 2023.3

Source:

3/26/2024
In the figure, points AA, BB, CC and DD are on the same line and are the centers of four tangent circles at the same point. Segment ABAB measures 88 and segment CDCD measures 44. The circumferences woth centers AA and CC are of equal size. We know that the sum of the areas of the two medium circles is equivalent to the sum of the areas of the small and large circles. What is the length of segment ADAD? https://cdn.artofproblemsolving.com/attachments/d/4/378243b9f4203e103af266e551eadccfc96adf.png
geometry