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Geometry Problem 487: Intersecting Circles, Area, Diameter, Parallel, 90 Degrees. High School, College, Math Education

The figure shows the circles of diameter AB and CD with line EAB parallel to CD. The measure of the arc CD is 90 degrees and A1, A2, and A3 are the areas of the shaded regions. Prove that A1 + A2 = A3.
 

Geometry Problem 487: Intersecting Circles, Area, Diameter, Parallel, 90 Degrees
 

 

 

See Also:

 

Intersecting Circles Index

 

Triangle, Cevian, Circle, Concurrency

Problem 488.
Triangle, Cevian, Concurrency, Circle, Circumcircle.

 

Tangent circles, Midpoint, Arc, Collinear

Problem 486.
Tangent circles, Chord, Arc, Midpoint, Collinearity, Congruence.

 

Square, Circles, Tangent

Problem 485.
Square, Side, Circles, Tangent, Radius, Measurement.

 

Square, Angle, 90 degrees, Proportion

Problem 484.
Square, Angle, 90 degrees, Triangle, Measurement, Proportion.

 

Triangle, Square, 90 degrees

Problem 483.
Square, Angle, 90 degrees, Measurement.

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