Monday, September 22, 2008

Elearn Geometry Problem 182

Overlapping Circles

See complete Problem 182 at:

Overlapping Circles, Find an angle. Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.


  1. x=(180°-mDAG)/2=(180°-mDAB-mBAE)/2=(180°-60°-45°)/2=37.5°

  2. Connect AB, AD, and BD, revealing Equilateral Triangle ABD; (AB=AD=BD=r, Angle BAD=60°) and AB is perpendicular to EF and =EB, (any line, ray, or segment crossing circle center is always perpendicular to the tangent point where it meets at,) Angle BAE=45°. Thus Angle DAG=Angle BAD+Angle BAE=(60+45)°=105°.
    Since DAG is isoceles, (AD=AD=r,)
    Therefore, Angle AGD=((180-105)/2)°=Angle x=37.5°.