Alternate Segment Theorem

[archiebear]

"The angle between a tangent and a chord drawn from the point of contact is equal to any angle in the alternate segment"
Can someone please elaborate on this, what does it mean by "in the alternate segment"?

I don't understand how these angles are alternate to each other
Some help please?

[Syndicate]

"The angle between a tangent and a chord drawn from the point of contact is equal to any angle in the alternate segment"
Can someone please elaborate on this, what does it mean by "in the alternate segment"?
(Image removed from quote.)
I don't understand how these angles are alternate to each other
Some help please?

Hey,

So a segement is the area, outside the triangle, but inside the circle. What your question means to say is that all the segments (there are 3 segemtns here) has the same angle, thus you have an equalaterial triangle. You will need a bit of knowledge of angles made in parallel lines, which are cut off by a transveral line. There is a lot of information loaded here about that: http://www.mathwarehouse.com/geometry/angle/parallel-lines-cut-transversal.php

[archiebear]

Hey,

So a segement is the area, outside the triangle, but inside the circle. What your question means to say is that all the segments (there are 3 segemtns here) has the same angle, thus you have an equalaterial triangle. You will need a bit of knowledge of angles made in parallel lines, which are cut off by a transveral line. There is a lot of information loaded here about that: http://www.mathwarehouse.com/geometry/angle/parallel-lines-cut-transversal.php

uhh, it's not necessarily an equilateral triangle, if theta was say for example, 40 degrees, it would not be an equilateral triangle.
Also, there are no parallel lines shown in this diagram, what i'm really asking for is how theta in this case is alternate to the other theta and why are they equal.
Thanks

[wyzard]

"The angle between a tangent and a chord drawn from the point of contact is equal to any angle in the alternate segment"
Can someone please elaborate on this, what does it mean by "in the alternate segment"?
(Image removed from quote.)
I don't understand how these angles are alternate to each other
Some help please?

The "alternate" in the alternate segment theorem refers to the segment on the other side of segment containing the tangent's angle. Notice how the angle is sandwiched between the 2 segments on other side. It's just a conventional theorem name in maths, you can call it "Other side angle theorem" if that makes it easier for you to visualize