SOLUTION: A triangle ABC is inscribed in a circle, and the tangent to the circle at C is parallel to the bisector of angle ABC. a Find the magnitude of ∠BCX. b Find the magnitude o

Question 1120605: A triangle ABC is inscribed in a circle, and the tangent
to the circle at C is parallel to the bisector of angle ABC.
a Find the magnitude of ∠BCX.
b Find the magnitude of ∠CBD, where D is the point of
intersection of the bisector of angle ABC with AC.
c Find the magnitude of ∠ABC.
Diagram: https://i.imgur.com/pGmnqPy.png
I'm unsure what tangent theorems to apply. All i know is that angle BCX is equal to angle CBD (parallel lines).
Thanks
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
arc BC is 80 degrees.
That means angle BCX is also 40 degrees. Tangents to a circle have an angle equal to half the arc. Parallel lines with equal alternate interior angles and CBD is 40 degrees. ABD is 40 degrees, because it is bisected. ABC is 80 degrees.

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SOLUTION: A triangle ABC is inscribed in a circle, and the tangent to the circle at C is parallel to the bisector of angle ABC. a Find the magnitude of &#8736;BCX. b Find the magnitude o

SOLUTION: A triangle ABC is inscribed in a circle, and the tangent to the circle at C is parallel to the bisector of angle ABC. a Find the magnitude of ∠BCX. b Find the magnitude o