Problem Solving

An equilateral triangle ABC is inscribed in circle ,If length of arc ABC is 24, What is approximate diameter.

A 11
B 13
C 15
D 22
E 25

Hi Anurag....
only thing m still missing on this is how arc ABC is 2/3 of circumferenc of circle

what i was getting 1/3 i.e 120/360

pls help ..

B166418

The ARC ABC will include all the three vertices of the triangle. Hence, Arc ABC will be 2/3 of the total circumference of the circle.

What you have considered will be any of the arcs AB, BC or CA.

also since triangle ABC is equilateral then the arcs AB, BC and CA will be equal.

So arc ABC = arc AB + arc BC

Hope this helps.

Hi Kaustubh..
Is there any other way to solve this question apart from

length of arc = circumfrence of circle * Q\360

so here Q is 240 ?

B166418 wrote:An equilateral triangle ABC is inscribed in circle ,If length of arc ABC is 24, What is approximate diameter.

A 11
B 13
C 15
D 22
E 25

As triangle ABC is equilateral, arc ABC is 2/3 of the circumference of the circle.
Arc ABC = 2/3 * Circumference

24 = 2/3 * Circumference

Circumference = 36

Circumference = 2* pi*r

2* pi*r = 36

Diameter = 2 *r

=> diameter * pi = 36
=> diameter = 36/pi
=> diameter = 36/3 (pi is 22/7 which is approximately 3)

Hence, diameter of the circle = 36/π = Slightly less than 36/3 ≈ 11

The correct answer is A.

B166418 wrote:Hi Kaustubh..
Is there any other way to solve this question apart from

length of arc = circumfrence of circle * Q\360

so here Q is 240 ?

Nice question, frankly the method that we are using seems to be the quickest approach. But I am working on another approach too (only after you asked). But let me tell you, things will get more complicated.

However, if you draw the figure for the question, you can just solve by looking at it. There is no need to write anything.

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Please have a look at this approach, nothing new, just a modification of the original approach.

we know that arc ABC = 24
also since triangle ABC is equilateral. all the three arcs are equal hence for arc AB

we solve

(120/360)*pi*D=12

solve this and you will get D~11

Here's d missing link

I solved this question by this method but took length of arc as given i.e 24 .

When I will stop doing silly mistakes

B166418 wrote:Here's d missing link

I solved this question by this method but took length of arc as given i.e 24 .

When I will stop doing silly mistakes

The day you will realise that "ITS NOW OR NEVER".

or
"Today will be that day
Not tomorrow, not next week but right now, right here"

That's some kind of motivational words...

Thanks pal