Problem:
In the figure shown below, major arc AD and minor arc BC have the same center O. Also, A lies between O and B, and D lies between O and C. Major arc AD, minor arc BC, and each of the two segments AB and CD have length 2Ο.
What is the distance from O to A?
Answer Choices:
A. 1
B. 1βΟ+1+Ο2β
C. 2Οβ
D. 21β1+Ο2β
E. 2
Solution:
Let β DOA=ΞΈ in radians, OA=r1β, and OB=r2β. Using s=rΞΈ, we get:
r1β(2ΟβΞΈ)=2Ο
r2βΞΈ=2Ο
r2ββr1β=2Ο
Substituting r2β=r1β+2Ο into r2βΞΈ=2Ο gives ΞΈ=r1β+2Ο2Οβ. Substituting this into the first equation:
