Because I couldn't get any help on the last problem I got a whole bunch more.  Could someone please help with this?


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 = 43 degrees, find angle CED, in degrees.

AnonymousConfusedGuy  Apr 27, 2018

Angle BAE  = 43°   ...so   minor  arc BE  will = 86°


And angle CBE  = 1/2 of this arc  = 43°


But.......since  CB and  CE  are tangents  to  the circle from a common point C....they are equal


Thus...in triangle BCE....BC  = EC...and the angles opposite these sides are also equal...


So angle CBE  = angle BEC


And  note that in triangle AEB.....angle AEB  intercepts a diameter....so its measure   = 90°


But  angle AEB  + angle BEC  + angle CED  = 180°.....so....


90   +   43   +   angle CED   = 180


133 + angle  CED  = 180        subtract   133 from each side


angle CED  =  47°



cool cool cool

CPhill  Apr 27, 2018
edited by CPhill  Apr 27, 2018
edited by CPhill  Apr 28, 2018

Merci beaucoup Monsieur!

AnonymousConfusedGuy  Apr 27, 2018

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