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Circle Gamma is the incircle of triangle ABC and is also the circumcircle of triangle XYZ. The point X is on BC, the point Y is on AB, and the point Z is on AC. If angle A=40 degrees, angle B=60 degrees, and angle C=80 degrees, what is the measure of angle YZX?

 Jan 13, 2019

See the following image :





Let D be the center of the circle

Since BA and BC are tangents meeting radii DX and DY.....then....

Angle BYD = Angle BXD = 90°

And angle YBX = 60°

And XBYD is a quadrilateral.....so the sum of its interior angles = 360

So angle YDX = 360 - 90 - 90 - 60  = 120°

And YDX is a central angle in the circle

And angle YZX is an inscribed angle in the circle intercepting the same arc as angle YDX

So....its measure is (1/2)YDX  = 60°




cool cool cool

 Jan 13, 2019
edited by CPhill  Jan 13, 2019
edited by CPhill  Jan 14, 2019

Nice pic Chris :)

Melody  Jan 13, 2019

Thanks, Melody...!!!!


.....it took me long enough to make it in GeoGebra......this utility is still kinda' funky to use...IMHO....



cool cool cool

CPhill  Jan 14, 2019
edited by CPhill  Jan 14, 2019

Yes I have a lot of fun using Geogebra too. 

I am still finding new functions in there. It can really do a lot of things. 


For anyone that is interested,it is a free download.

Melody  Jan 14, 2019

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