arclength of circle with equilateral triangle

[asadullah100]

kindly help me out in solving this problem.. your response will be highly appreciated... what will be the angle for this in arclength formula.... the correct answer was 11 in gmat prep... thanks...


Q: what is the approximate diameter of a circle with an equilateral triangle ABC inside it having arclength ABC equal to 24?

[lalitkc]

Q: what is the approximate diameter of a circle with an equilateral triangle ABC inside it having arclength ABC equal to 24?

Let O be the centre of the circle.
In equilateral triangle ABC,
<ABC = 60 ,
<AOC = 2 <ABC = 120 .....property : central angle = 2 * inscribed angle
l (arc) / circumference = central angle / 360
l (arc AC) = 12
120/360 = 12/ (Pi * d)
d= 11.45

[geetesht]

Q: what is the approximate diameter of a circle with an equilateral triangle ABC inside it having arclength ABC equal to 24?

Let O be the centre of the circle.
In equilateral triangle ABC,
<ABC = 60 ,
<AOC = 2 <ABC = 120 .....property : central angle = 2 * inscribed angle
l (arc) / circumference = central angle / 360
l (arc AC) = 12
120/360 = 12/ (Pi * d)
d= 11.45

lalit,

how about we juz use this formula after having derived the central angel as 120

(240/360 ) * 2 pi radius = 24 (Length of arc ABC)

OR

(2/3) * pi Diameter = 24

OR

Diameter = (24 * 3)/(2 pi)

Diameter = 11.45

[RonPurewal]

co-ordinate-gprep-t2660.html

please search the forum!

not only will this help us avoid multiple posts on the same problem, but you'll get feedback instantly instead of having to wait.