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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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Math Expert
Joined: 02 Sep 2009
Posts: 58445
Points A,B,C lie on the circle. Point O is the center of the circle an  [#permalink]

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07 Jan 2015, 07:38
00:00

Difficulty:

35% (medium)

Question Stats:

77% (01:32) correct 23% (01:44) wrong based on 112 sessions

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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.

Attachment:

2015-01-07_1837.png [ 3.46 KiB | Viewed 1881 times ]

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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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07 Jan 2015, 11:28
1
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.

Attachment:
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]

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08 Jan 2015, 00:41
2

Attachment:

2015-01-07_1837.png [ 3.85 KiB | Viewed 1679 times ]

$$\triangle$$ 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]

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08 Jan 2015, 02:49
2
Area of the triangle = 8

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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Joined: 02 Sep 2009
Posts: 58445
Re: Points A,B,C lie on the circle. Point O is the center of the circle an  [#permalink]

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09 Jan 2015, 06:50
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.

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]

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18 Dec 2018, 02:17
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Re: Points A,B,C lie on the circle. Point O is the center of the circle an   [#permalink] 18 Dec 2018, 02:17
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