Problem Solving

If an equilateral triangle ABC is inscribed in a circle .Length of Arc ABC =24
Wht is the diameter of circle.

Im getting ans 24
OA is 11

I got 11.464 approx equal to 11 but I am not sure if what I did is the right approach....

I have attached a diagram and steps...I am sure there is a better approach...

pls reply

why u have taken other angle 240 what is wrong with my sol

Vivek,

By taking 120 degrees, you are measuring the arc length of AC (in my diagram attached, that is the dotted line) while you dont know what that value is. The only info you know is about arc ABC (the dark solid line).

Since 120 + x = 360 at the center, x = 240.

As you already know the length of an arc = angle at the center formed by the two radii intersecting (OA and OB).

240 is the angle that complements the 120 in the center.

So, 240/360 * 2 pi r = 24

2 pi r or pi * d = 36

d = 36/pi = 11.46

Hope this helps.

Refer

https://www.beatthegmat.com/equilateral- ... tml#112083

Sonu,
cn u explain this in my diagram,coz in my diagram 120 degree include whole ABC arc...

In your diagram, your 120 is the angle referring to bottom portion of the circle (the portion below the base of your triangle) - arc AC, no info is given about that.

All we know if about length of arc ABC (24) - the top portion - the portion from the base of your triangle all the way around the circle, whose angle at the center is 240.

So, 240/260 * 2 pi r = 24