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.
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
3 answers
length of the arc ... 285/360 * 2 * π * 10
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!
2 answers