How Do Tangents and Chords Affect Angles in Circles?

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Homework Help Overview

The discussion revolves around the relationships between angles formed by tangents and chords in a circle, specifically focusing on a geometric problem involving angles and their measures. Participants are analyzing the properties of isosceles triangles and inscribed angles in the context of the problem presented.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants attempt to determine the measures of various angles based on given information and properties of triangles. Questions arise regarding the equality of certain angles and the implications of the tangent line in the problem.

Discussion Status

The discussion is active, with participants exploring different interpretations of the problem. Some guidance has been offered regarding the significance of the tangent and its relationship to the angles, but there is no explicit consensus on the correct approach or solution yet.

Contextual Notes

There is uncertainty regarding the equality of segments and the implications of the tangent line, which are critical to solving the problem. Participants are also considering whether additional information is provided in the problem statement that could aid in their reasoning.

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Homework Statement


http://i41.tinypic.com/35mno6v.jpg


2. The attempt at a solution
So far, I found out that angle 4 and 5 is 55, because angle D is 110.. but I don't know if that's right. Please help!
 
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Angle BDA is 110 degrees, because angle 1 is 70 degrees. Angles 4 and 5 are equal, because triangle BDA is isosceles. Angles 4, 5 and BDA have to add to 180 degrees, which they don't do if angles 4 and 5 are 55 degrees each.
 
What about angle 2 and 3? My answer was 55 for both of them..
 
Those would be correct if triangle BCD is isosceles, with BD = CD. Can you establish that equality somehow?
 
Hmm, I suppose I can't. Now I've hit the bricks, I don't know how to figure it out.
 
Is there any other information given in this problem, such as at the top of the set of problems?

One thing I haven't used is the statement that AB is tangent at B. I don't understand why this is significant or how it ties into this problem.
 
Once you have angle 4/5 you can easily figure out 2 using inscribed angles and angles formed by tangents.
 
Mark44 said:
One thing I haven't used is the statement that AB is tangent at B. I don't understand why this is significant or how it ties into this problem.

It is significant because an angle formed by a chord and a tangent to a circle is half the arc it intercepts. Angles 2 and 4 are inscribed angles that intercept the same arc, so they are congruent.
 

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