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Triangle EFG is inscribed in the circle with center O and radius 4.

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itwasmaroon
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Triangle EFG is inscribed in the circle with center O and radius 4. [#permalink] New post   Updated on: 28 Jun 2024, 22:17
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GRE Triangle EFG is inscribed in the circle.jpg [ 13.74 KiB | Viewed 170 times ]


Triangle EFG is inscribed in the circle with center O and radius 4.

Quantity A
Quantity B
The area of triangular region EFG
12




A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
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Official Answer
D

Originally posted by itwasmaroon on 28 Jun 2024, 14:59.
Last edited by Carcass on 28 Jun 2024, 22:17, edited 1 time in total.
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Re: Triangle EFG is inscribed in the circle with center O and radius 4. [#permalink] New post   28 Jun 2024, 22:43
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Hi

are you sure the answer is D? For my understanding should be A
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teshu325
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Re: Triangle EFG is inscribed in the circle with center O and radius 4. [#permalink] New post   02 Jul 2024, 05:10
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Can anyone please explain how is D the correct ans?

As per my understanding, radius is OE, OG and OF = 4

therefore, in triangle EFG,
base= EG= 8
height = OF= 4

therefore, area = 1/2 * base * height
= 1/2 * 8 *4
=16

hence, A> B

Please let me know if I made any mistake in understanding?
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Re: Triangle EFG is inscribed in the circle with center O and radius 4. [#permalink] New post   02 Jul 2024, 05:15
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I think there is agreement that A is the answer. The fact that we do have specific numbers means D cannot be the answer in any case.

We have precise refernces
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itwasmaroon
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Re: Triangle EFG is inscribed in the circle with center O and radius 4. [#permalink] New post   02 Jul 2024, 10:04
teshu325 how can OF be the height? Carcass kindly share your solution
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teshu325
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Re: Triangle EFG is inscribed in the circle with center O and radius 4. [#permalink] New post   02 Jul 2024, 10:08
itwasmaroon

why not? we can draw a line and make OF as height!
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Re: Triangle EFG is inscribed in the circle with center O and radius 4. [#permalink] New post   02 Jul 2024, 10:10
teshu325 height must be perpendicular to the base.
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Re: Triangle EFG is inscribed in the circle with center O and radius 4. [#permalink] New post   02 Jul 2024, 10:21
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My solution

Attachment:
GRE triangle area.jpg
GRE triangle area.jpg [ 132.31 KiB | Viewed 73 times ]


We know the radius that is 4. Therefore, the other radius is also 4. An d the diameter is 2R=8

The height of the triangle is also the radius, which is 4

We can calculate the area of the 1 and 2 triangle

\(A=\frac{ 1}{2}* b*h=\frac{1}{2}*4*4=8
\)

Add up the two areas \(8+8=16
\)

A is the answer.

I do not see any other possible solution
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Re: Triangle EFG is inscribed in the circle with center O and radius 4. [#permalink] New post   02 Jul 2024, 10:25
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itwasmaroon wrote:
teshu325 height must be perpendicular to the base.


Not true in the sense we do not have any information about its scale.

The figure could be also this way and the height is perpendicular to the base


Attachment:
GRe triangle area 2.jpg
GRe triangle area 2.jpg [ 191.42 KiB | Viewed 71 times ]
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