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Points A,B,C lie on the circle. Point O is the center of the circle an

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Bunuel
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Points A,B,C lie on the circle. Point O is the center of the circle an [#permalink] New post   07 Jan 2015, 07:38
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Points A,B,C lie on the circle. Point O is the center of the circle and lies on the line segment AB. The area of triangle BOC is 8 square inches. If angle COB is 90 degrees then the diameter of the circle equals to

A. 1 inch
B. 2 inches
C. 4 inches
D. 6 inches
E. 8 inches


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E
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PareshGmat
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Re: Points A,B,C lie on the circle. Point O is the center of the circle an [#permalink] New post   08 Jan 2015, 00:41
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Answer = E. 8 inches

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\(\triangle\) COB is an isosceles right angle triangle with CO = OB = radius of the circle

Let diameter = d

\(Area = \frac{1}{2} (\frac{d}{2})^2 = 8\)

\(\frac{d}{2} = 4\)

d = 8
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Re: Points A,B,C lie on the circle. Point O is the center of the circle an [#permalink] New post   08 Jan 2015, 02:49
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Area of the triangle = 8

Let the radius = r
In triangle COB -
Area is given by = 1/2( r*r) Sin90 -----> (Sin90 = 1)

1/2(r*r) = 8
r*r = 16
r = 4

Diameter = 2*r = 8
Option E
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Re: Points A,B,C lie on the circle. Point O is the center of the circle an [#permalink] New post   07 Jan 2015, 11:28
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Bunuel wrote:

Tough and Tricky questions: Geometry.




Points A,B,C lie on the circle. Point O is the center of the circle and lies on the line segment AB. The area of triangle BOC is 8 square inches. If angle COB is 90 degrees then the diameter of the circle equals to

A. 1 inch
B. 2 inches
C. 4 inches
D. 6 inches
E. 8 inches

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2015-01-07_1837.png


1/2 b * h = 8 => b*h = 16

Since b=h as both are radius of the circle

b^2 = 16
b = 4 = r

Diameter d= 2r = 8

Ans E
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Re: Points A,B,C lie on the circle. Point O is the center of the circle an [#permalink] New post   09 Jan 2015, 06:50
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Bunuel wrote:

Tough and Tricky questions: Geometry.




Points A,B,C lie on the circle. Point O is the center of the circle and lies on the line segment AB. The area of triangle BOC is 8 square inches. If angle COB is 90 degrees then the diameter of the circle equals to

A. 1 inch
B. 2 inches
C. 4 inches
D. 6 inches
E. 8 inches

Kudos for a correct solution.

Show Spoiler
Attachment:
2015-01-07_1837.png


OFFICIAL SOLUTION:

(E) Angle COB is 90 degrees so triangle COB is a right triangle. Its area is 1/2 × OC × OB. Point O is the center of the circle therefore OB and OC are radii. We know the area of triangle COB, it is 8 square inches, so we can find the radius r from equation:

1/2 × r × r = 8
r² = 16
r = 4 inches (r can not be -4 because r must be positive).

The diameter is twice the radius, so the answer is 8 inches, choice (E).
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Re: Points A,B,C lie on the circle. Point O is the center of the circle an [#permalink] New post   21 May 2022, 19:44
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Re: Points A,B,C lie on the circle. Point O is the center of the circle an [#permalink]
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