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

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New post 07 Jan 2015, 06:38
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A
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D
E

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Question Stats:

79% (01:13) correct 21% (01:23) wrong based on 98 sessions

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Tough and Tricky questions: Geometry.



Image
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.

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2015-01-07_1837.png
2015-01-07_1837.png [ 3.46 KiB | Viewed 1655 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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New post 07 Jan 2015, 10:28
1
Bunuel wrote:

Tough and Tricky questions: Geometry.



Image
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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New post 07 Jan 2015, 23:41
2
Answer = E. 8 inches

Attachment:
2015-01-07_1837.png
2015-01-07_1837.png [ 3.85 KiB | Viewed 1455 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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New post 08 Jan 2015, 01:49
2
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]

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New post 09 Jan 2015, 05:50
Bunuel wrote:

Tough and Tricky questions: Geometry.



Image
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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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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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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Re: Points A,B,C lie on the circle. Point O is the center of the circle an &nbs [#permalink] 18 Dec 2018, 01:17
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