Tangents

H

Hockeyman

Junior Member
Joined
Dec 8, 2005
Messages
79
Rays WM and WN are tangents to circle P. A central angle of 130 degrees is given, what would the value of angle w be? I think the answer is 50 degrees.
 
The measure of \(\displaystyle \begin{array}{l}
m(\angle W) = \frac{1}{2}\left( {m(\mbox{majorarc}) - {m(\mbox{minorrarc})} \right) \\
m(\angle A) = {m(\mbox{minorarc}) \\
\end{array}\)
 
That's a really nice answer. Too bad no one knows how you arrived at it.
 
I would have shown how i had gotten it but it is hard to explain it without being able to draw it, and i probably just would have confused you guys even more. But i'm pretty sure it is right, so i was just looking for someone to double check because i could have made a mistake.
 
Give it a shot, anyway. If nothing else, you will learn to communicate better on each attempt.

If you wish to prove it to yourself:
1) Draw a line segment from W to the center of the circle.
2) This segment bisects the central angle (130º/2 = 65º) and the angle at W.
3) The angles at M and N are 90º. (Radius Intersecting a Tangent)
4) It's easily observed what is left for the two matching angles at W.
 
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