Online Geometry Problems

Online Geometry Problem 822: Circle, Semicircle, Arc, Chord, Midpoint, Sector, Triangle, Area. Level: High School, SAT Prep, College, Mathematics Education

The figure below shows a semicircle O with diameter AB = 12. Arc AC = 135 degrees and D is the midpoint of chord AC. Find the shaded area bounded by CD, BD and arc BC.


 

Circle, Semicircle, Diameter, Chord, Midpoint Area


 

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.

 

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