 # Online Geometry Problem 1084: Circle, Chord, Radius, Diameter, Parallel lines, 45 Degrees, Angle, Metric Relations. Level: High School, SAT Prep, College, Mathematics Education

< PREVIOUS PROBLEM  |  NEXT PROBLEM >

 The figure below shows a circle of radius r, chords AB and CD are parallel, chords BC and DE parallel. If angle ABC = 45 degrees, AB = a, BC = b, CD = c, and DE = d, prove that a2 + c2 = b2 + d2 = 4r2. Geometry problem solving is one of the most challenging skills for students to learn. When a problem requires auxiliary construction, the difficulty of the problem increases drastically, perhaps because deciding which construction to make is an ill-structured problem. By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as "given."

Home | SearchGeometry | Problems | All Problems | Open Problems | Visual Index | 10 Problems | 1081-1090 | Circle | Triangle | Diameter | Parallel lines45 degrees | Email | Solution / comment | by Antonio Gutierrez
Last updated: Feb 15, 2015