yankees660 wrote:"in the figure above, equilaterial triangle ABC is inscribed in the circle. if the length of arc ABC is 24, what is the approximate diameter of the circle"
the drawing is a circle with a regular equilateral triangle inscribed, A to the left, B at the top, C to the right
a - 5
b - 8
c- 11
d- 15
e - 19
OA = C
thanks for the help!
The solution relies on 4 properties and 1 formula:
1) Each angle in an equilateral is 60 degrees
2) The measure of an arc is always twice the measure of the remote angle that forms the arc.
3) An entire circle is 360 degrees
4) Length of an arc is proportional to its degree measure
5) circumference = 2*pi*diameter.
Since angle B=60, minor arc AC must be 120 (1/3 of the circle), so the remainder of the circle (arc ABC) must be 2/3 of the circle. Since this arc is a length of 24, 2/3 of the circle is 24, so the circumference must be 36.
With the circumference, it's easy to find the diameter. The answer is
C
You can see a detailed solution with graphs as well as a video solution at
GMATPrep Question 1304. If you struggle with this type of question, use the Drill Engine to generate timed drills and set topic='geometry' and difficulty='400-500 AND 500-600'
Good Luck
-Patrick
