MathDB

7

Part of 2003 AIME Problems

Problems(2)

Possible perimeters

Source:

5/11/2006
Point BB is on AC‾\overline{AC} with AB=9AB = 9 and BC=21BC = 21. Point DD is not on AC‾\overline{AC} so that AD=CDAD = CD, and ADAD and BDBD are integers. Let ss be the sum of all possible perimeters of △ACD\triangle ACD. Find ss.
geometryperimeterinequalitiestrigonometryperpendicular bisectorPythagorean Theorem
Area of a Rhombus

Source:

12/26/2006
Find the area of rhombus ABCDABCD given that the radii of the circles circumscribed around triangles ABDABD and ACDACD are 12.512.5 and 2525, respectively.
geometryrhombustrigonometrytrig identitiesLaw of Sines