MathDB

4

Part of 2001 AIME Problems

Problems(2)

Angle Bisector

Source:

12/6/2005
In triangle ABCABC, angles AA and BB measure 60 degrees and 45 degrees, respectively. The bisector of angle AA intersects BC‾\overline{BC} at TT, and AT=24.AT=24. The area of triangle ABCABC can be written in the form a+bc,a+b\sqrt{c}, where aa, bb, and cc are positive integers, and cc is not divisible by the square of any prime. Find a+b+c.a+b+c.
geometrytrigonometrytrig identitiesLaw of Sines
Coordinates Problem

Source:

12/28/2006
Let R=(8,6)R=(8,6). The lines whose equations are 8y=15x8y=15x and 10y=3x10y=3x contain points PP and QQ, respectively, such that RR is the midpoint of PQ‾\overline{PQ}. The length of PQPQ equals mn\frac{m}{n}, where mm and nn are relatively prime positive integers. Find m+nm+n.
analytic geometrynumber theoryrelatively prime