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Let AB be a diameter of a circle centered at O. Let E be a point on the circle, and let the tangent at B intersect the tangent at E and AE at C and D, respectively. If angle BAE = 41 degrees, find angle CED, in degrees.

 

 Nov 20, 2020
 #1
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Angels BAE, CBE, and BEC are congruent.

 

angle CED = 90 - 41

 Nov 20, 2020
 #2
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Since BE and EC  are tangents drawn from C, they are equal

 

And since BAE  = 41.....then CBE  = 41

And minor arc BE  = 82 

Then CEB  equals half of this  =  41

 

But AEB  = 90  since A and  B are diameter endpoints

 

So CED  =  180 -90  - 41  =   90 - 41   =  49°

 

cool cool cool 

 Nov 20, 2020

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