Asked by taylor
two tangents to a circle form an angle of 105 degrees. find the length of the major arc if the radius if the circle is 10 inches
Answers
Answered by
oobleck
Draw a diagram. Label the points of tangency A and B, and the intersection of the tangents, label T. The center of the circle is O.
Then angle T = 105°
angle OTA = OTB = 52.5°
triangles OBT and OAT are right triangles, so
angle TOA = TOB = 37.5°
so, angle AOB = 75°, making the major arc 285°
The radius of the circle does not matter.
Then angle T = 105°
angle OTA = OTB = 52.5°
triangles OBT and OAT are right triangles, so
angle TOA = TOB = 37.5°
so, angle AOB = 75°, making the major arc 285°
The radius of the circle does not matter.
Answered by
R_scott
length of the arc ... 285/360 * 2 * π * 10
Answered by
oobleck - @R_scott
Nice catch. I was just figuring the angular measure of the arc, not its length.
I wondered why they gave the radius!
I wondered why they gave the radius!
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.