MathDB

13

Part of 2001 AIME Problems

Problems(2)

Arcs

Source: AIME 2001 #13

12/6/2005
In a certain circle, the chord of a dd-degree arc is 22 centimeters long, and the chord of a 2d2d-degree arc is 20 centimeters longer than the chord of a 3d3d-degree arc, where d<120.d<120. The length of the chord of a 3d3d-degree arc is −m+n-m+\sqrt{n} centimeters, where mm and nn are positive integers. Find m+n.m+n.
quadraticstrigonometrygeometrysimilar triangles
Chasing Lengths in Quadrilateral

Source:

12/28/2006
In quadrilateral ABCDABCD, ∠BAD≅∠ADC\angle{BAD}\cong\angle{ADC} and ∠ABD≅∠BCD\angle{ABD}\cong\angle{BCD}, AB=8AB=8, BD=10BD=10, and BC=6BC=6. The length CDCD may be written in the form mn\frac{m}{n}, where mm and nn are relatively prime positive integers. Find m+nm+n.
number theoryrelatively prime