Geometry problem - Curcumference of a circle

1. not sufficient --> we cannot use given arc lenght because it might vary for different angles
2. not sufficient -- > not sufficient data given to compute cir.

Both 1 & 2 sufficient -- > If r=s, then it becomes an equilateral triangle and we can make another similar equilateral triangle with XYZ. As this is inscribed in circle, it divides the circle arc into 3 parts. Hence,

2/3 * Circumference = 18 --> Cir = 27.

IMO, the answer is C.

What is the OA ?

I got it (I thought r as y, so got confused) anyways, thanks.

OA:C

sasi78 wrote:1. not sufficient --> we cannot use given arc lenght because it might vary for different angles
2. not sufficient -- > not sufficient data given to compute cir.

Both 1 & 2 sufficient -- > If r=s, then it becomes an equilateral triangle and we can make another similar equilateral triangle with XYZ. As this is inscribed in circle, it divides the circle arc into 3 parts. Hence,

2/3 * Circumference = 18 --> Cir = 27.

IMO, the answer is C.

What is the OA ?

I am really flummoxed. Please help! How can r=s along with (i) help to solve the question. Isn't r radius and s the angle YXZ and YZX?

I am missing something...

kanha81 wrote:

sasi78 wrote:1. not sufficient --> we cannot use given arc lenght because it might vary for different angles
2. not sufficient -- > not sufficient data given to compute cir.

Both 1 & 2 sufficient -- > If r=s, then it becomes an equilateral triangle and we can make another similar equilateral triangle with XYZ. As this is inscribed in circle, it divides the circle arc into 3 parts. Hence,

2/3 * Circumference = 18 --> Cir = 27.

IMO, the answer is C.

What is the OA ?

I am really flummoxed. Please help! How can r=s along with (i) help to solve the question. Isn't r radius and s the angle YXZ and YZX?

I am missing something...

I'm in the same boat I don't understand why it would mention anything about r. I thought the y was r, if it was then you would have enough info to solve the equation.

What does r stand for? Radius? Why would it give an angle measure equal to a length?

The drawing misled you guys, since it's really small. That "y" you see on the picture is actually an "r" and it's just a random letter used to designate angle XYZ.

The notation is: r is the measurement of angle XYZ.

As you may imagine, you can't have r as radius, since it's impossible to say "length" = "measurement of angle" (it would be like comparing horses to chicken) in statement 2. r has to be an angle as well, since you only compare angles to angles.

sasi78 wrote:1. not sufficient --> we cannot use given arc lenght because it might vary for different angles
2. not sufficient -- > not sufficient data given to compute cir.

Both 1 & 2 sufficient -- > If r=s, then it becomes an equilateral triangle and we can make another similar equilateral triangle with XYZ. As this is inscribed in circle, it divides the circle arc into 3 parts. Hence,

2/3 * Circumference = 18 --> Cir = 27.

IMO, the answer is C.

What is the OA ?

This might be a silly question, but "how" or "why" do you multiply the circumference by 2/3?

Isn't -
arc length = 18 = (n/360) * 2 * pi * r, where n=60

hey kanha18,

if you see the circle, it is made of three arcs-XY, YZ, XZ

statement 2 says r=s given that the base angles (s) are equal, that makes the triangle XYZ an equilateral triangle (easy to see if you join XZ, angle YXZ=s and angle YZX=s, r=s)

so all arcs would be equal in length=>XY=YZ=XZ

(XY+YZ+XZ=circumference)
so XY+XZ forms 2/3 of the circumference