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

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The figure shows circles C1 and C2, tangent at C. Chord DE and C2 are tangent at F, G is the midpoint of arc DE and DH is tangent to C2, at H. Prove that (1) Points G, F, and C are collinear, (2) GD, GE, and GH are congruent.
 

Tangent Circles, Midpoint, Chord, Collinearity, Congruence
 

 

 

See Also:

 

Tangent Circles Index

 

Circle, Area, 90 Degrees

Problem 487.
Intersecting Circles, Area, Diameter, Parallel, 90 Degrees.
 

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.
 

Triangle, Circumcircle, Incircle, Excircle

Problem 482.
Triangle, Circumcircle, Incenter, Excenter, Midpoint, Cyclic Points.

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