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# Help!

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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

#1
+111437
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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°

Jan 13, 2019
edited by CPhill  Jan 13, 2019
edited by CPhill  Jan 14, 2019
#2
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Nice pic Chris :)

Melody  Jan 13, 2019
#3
+111437
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Thanks, Melody...!!!!

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

CPhill  Jan 14, 2019
edited by CPhill  Jan 14, 2019
#4
+110116
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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.