Line CD is tangent to circle A at point B. segment AB is a radius of circle A. what can be concluded about angle ABD?

i don't know

2 Answers
Lucy
Jun 20, 2018

#angle ABD=90#

Explanation:

![https://useruploads.socratic.org/CchLlAgxS9ipEK1XPGWo_tangent_to_circle_is_perpendicular_to_radius.jpg)

Above is a diagram that basically describes what is going on in the question.

Notice the line that is touching the circle at one point. That is your line CD

The point B is the point where your tangent CD touches the circle

Now since it tells you that the segment AB is radius of the circle A, that means that the tangent CD is perpendicular to your segment AB ie the rule "tangent to circle is perpendicular to radius of the circle"

This means that #angle ABD=90#

Sirach
Jun 20, 2018

#m<ABD=90#; angle ABD is a right angle.

Explanation:

Because the angle is formed by the radius intersecting a line at point B, the point of tangency, and according to the converse of the Tangent to a Circle Theorem, the two line segments can be concluded to be perpendicular, thus forming a right angle.

Sources:
https://www.ck12.org/geometry/tangent-lines/lesson/Tangent-Lines-GEOM/
http://www.sparknotes.com/math/geometry1/circles/section3/

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