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25 Nov 2019, 02:19
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A
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Difficulty:
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Question Stats:
49% (02:28) correct
51%
(02:12)
wrong
based on 140
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If O is the center of the circle above and the length of chord AB is 2 units, what is the length of the arc ACB?
(1) The area of ΔOAB is \(\sqrt{3}\) square units
(2) The area of sector OACBO is \(\frac{2π}{3}\)
Are You Up For the Challenge: 700 Level Questions
Attachment:
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Bunuel
AB=2
OA=OB=r
To find the length ACB we need r and angle OAB
(1) The area of ΔOAB is \(\sqrt{3}\) square units sufic
Area ΔOAB = √3; ΔOAB is an equilateral or an isosceles triangle;
If ΔOAB is an equilateral triangle, \(area=r^2√3/4=√3…r=2…<OAB=60\)
If ΔOAB is an isosceles triangle with base AB, \(area=AB•h/2=√3…2h/2=√3…h=√3\)
A perpendicular from the O to AB would divide ΔOAB into two right angle triangles with:
base=1 height=√3… this is a special triangle 30:60:90 with sides x:x√3:2x or, 1:√3:2.
Now we have radius = 2 and <OAB = 60.
(2) The area of sector OACBO is \(\frac{2π}{3}\) insufic
\(<OAB=a\)
\(Area.Sector = πr^2(a/360)…πr^2(a/360)=2π/3…(r,a)=unknown\)
Ans (A)
27 Nov 2019, 09:40
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Statement 1.From the area and the base we can find the height. Since we know this is an isosceles/equilateral, the perpendicular/height to the base divides the base into 2 equal lengths ,dividing the triangle into two congruent triangles with legs 1 and \(\sqrt{3}\).from this we know we have a hypoteneuse of 2.In essence, we have a 90-60-30 triangle.Since we have the angle(=60) and the radius(=2) we can find the length of the arc.Sufficient
Statement 2 : to find the length of the arc, we need to multiply the area given by 2 and divide the result by the radius of the circle.We can not find the radius
with the information given us.Insufficient
Answer is A
Statement 2 : to find the length of the arc, we need to multiply the area given by 2 and divide the result by the radius of the circle.We can not find the radius
with the information given us.Insufficient
Answer is A
