MHB Finding Angle at $\gamma$ - Help Requested

  • Thread starter Thread starter Carla1985
  • Start date Start date
  • Tags Tags
    Angle
AI Thread Summary
To determine the angle at $\gamma$, the vertical angles theorem is suggested, but it may not directly apply if $\gamma$ is perceived as part of a circle's edge. The user expresses confusion, indicating that $\gamma$ should represent the angle formed by two intersecting lines rather than a segment of the circle. Clarification is sought on how to accurately calculate this angle. The discussion emphasizes the need for a clear understanding of angle definitions in relation to geometric figures. Overall, the conversation highlights the importance of correctly identifying the components involved in angle measurement.
Carla1985
Messages
91
Reaction score
0
View attachment 6256
Hi,

could someone please tell me what theorem I need to be looking at to work out the angle at $\gamma$ please? I've worked out the rest but can't find a theorem for this one.

Thanks
 

Attachments

  • General - 20161101_20115 p.m. - 10.png
    General - 20161101_20115 p.m. - 10.png
    26.7 KB · Views: 85
Mathematics news on Phys.org
Use the vertical angles theorem.
 
Euge said:
Use the vertical angles theorem.

Thanks but that just gives me the angle between the two straight lines. My impression was that $\gamma$ was the part of the angle up to the edge of the circle.
 
That would not make an angle, for an angle is formed by two straight lines. It would only make sense for $gamma$ to be the angle between those two lines.
 
Euge said:
That would not make an angle, for an angle is formed by two straight lines. It would only make sense for $gamma$ to be the angle between those two lines.

That would make things a whole lot easier. Thank you for your help!
 
Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
Is it possible to arrange six pencils such that each one touches the other five? If so, how? This is an adaption of a Martin Gardner puzzle only I changed it from cigarettes to pencils and left out the clues because PF folks don’t need clues. From the book “My Best Mathematical and Logic Puzzles”. Dover, 1994.

Similar threads

Back
Top