the circle it belongs to

[sanju09]

How far is point P from point Q?

(1) Chord PQ is same as radius and area of the circle it belongs to.

(2) Major-arc PQ of the circle it belongs to is 5/3.

[ymach3]

Is the answer - A ?


PQ= (Pi)^-1 ---> from S (i)

S(ii) - Insufficient as R and angle are unknown.

Please correct me if i did a blunder ...

[Fiver]

Agree with A.

St1] suggest that the lenght of PQ is 7/22

St2] is insufficient as it suggests more than one possibility-

e.g. the minor arc could be 90, making the triangle a 45-45-90 triangle and PQ = root2 * r
or the triangle could be an equilateral triangle, making PQ = r = 7/22

What's the OA?

[eaakbari]

(1) Chord PQ is same as radius and area of the circle it belongs to.
.

I cannot comprehend this statement. Someone please explain

[Cdawg]

How far is point P from point Q?

(1) Chord PQ is same as radius and area of the circle it belongs to.

(2) Major-arc PQ of the circle it belongs to is 5/3.

Statement 1:

if Area = radius = chord, it follows that A = r = Pi*r^2 => r=1/Pi so chord is 1/Pi No other circle fulfills the requirement that area equals radius. So the statement is sufficient

Statement 2: tells you that the major arc is 5/3 long. Well you don't know where the points are located on the circle. => insufficient

I think the question tries to trick you into combining both statements. Then you can also solve for it using the 5/3 that account for 5/6th of the whole circumference, which you can use to calculate the radius = chord. At least it tricked me

well, i agree with the previous posters

[Cdawg]

(1) Chord PQ is same as radius and area of the circle it belongs to.
.

I cannot comprehend this statement. Someone please explain

chord = radius = area

[kstv]

How far is point P from point Q?
(1) Chord PQ is same as radius and area of the circle it belongs to.
(2) Major-arc PQ of the circle it belongs to is 5/3.

(1) Length of PG = r = Pi r²
Pi r² - r = 0 r(22/7*r-1) = 0 so r = 7/22
Suff
(2) PQ = r if o is the centre of the circle PO= OQ = PQ
POQ is a equilateral triangle and angle POQ is 60°
so minor arc PQ is 1/6 of 2pi r
and major arc = 5/6 * 22/7 * 2 * r = 5/3
or r= 7/22 Suff
IMO D
Great Q

[sanju09]

How far is point P from point Q?
(1) Chord PQ is same as radius and area of the circle it belongs to.
(2) Major-arc PQ of the circle it belongs to is 5/3.

(1) Length of PG = r = Pi r²
Pi r² - r = 0 r(22/7*r-1) = 0 so r = 7/22
Suff
(2) PQ = r if o is the centre of the circle PO= OQ = PQ
POQ is a equilateral triangle and angle POQ is 60°
so minor arc PQ is 1/6 of 2pi r
and major arc = 5/6 * 22/7 * 2 * r = 5/3
or r= 7/22 Suff
IMO D
Great Q

How is (2) alone sufficient? Is it (1)'s hangover or something?