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Updated on: 01 Feb 2020, 10:35
Originally posted by MathRevolution on 28 Jan 2020, 01:02.
Last edited by MathRevolution on 01 Feb 2020, 10:35, edited 1 time in total.
Last edited by MathRevolution on 01 Feb 2020, 10:35, edited 1 time in total.
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
80% (02:00) correct
20%
(01:48)
wrong
based on 45
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[GMAT math practice question]
Point \(O\) is the circumcenter of triangle \(ABC\), and the length of \(AC\) is \(7\). The length of the perimeter of triangle \(OAC\) is \(19\). What is the area of the circumscribed circle of triangle \(ABC\)?
1.28ps.png [ 8.69 KiB | Viewed 2955 times ]
A. \(30 π\)
B. \(32 π\)
C. \(34 π\)
D. \(36 π\)
E. \(38 π\)
Point \(O\) is the circumcenter of triangle \(ABC\), and the length of \(AC\) is \(7\). The length of the perimeter of triangle \(OAC\) is \(19\). What is the area of the circumscribed circle of triangle \(ABC\)?
Attachment:
1.28ps.png [ 8.69 KiB | Viewed 2955 times ]
A. \(30 π\)
B. \(32 π\)
C. \(34 π\)
D. \(36 π\)
E. \(38 π\)
28 Jan 2020, 03:29
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MathRevolution
[GMAT math practice question]
Point \(O\) is the circumcenter of triangle \(ABC\), and the length of \(AC\) is \(7\). The length of the perimeter of triangle \(ABC\) is \(19\). What is the area of the circumscribed circle of triangle \(ABC\)?
A. \(30 π\)
B. \(32 π\)
C. \(34 π\)
D. \(36 π\)
E. \(38 π\)
Point \(O\) is the circumcenter of triangle \(ABC\), and the length of \(AC\) is \(7\). The length of the perimeter of triangle \(ABC\) is \(19\). What is the area of the circumscribed circle of triangle \(ABC\)?
Attachment:
1.28ps.png
A. \(30 π\)
B. \(32 π\)
C. \(34 π\)
D. \(36 π\)
E. \(38 π\)
Is the information given complete?
I mean, a triangle with one side 7 and perimeter 19 is not uniquely defined. Assuming integer sides, we can have 4 possible triangles having sides:
7, 6, 6
7, 7, 5
7, 8, 4
7, 9, 3
Except the last one, all 3 are acute angled triangles, and so, will have the circum-center inside the triangle as shown in the diagram.
In each case, the circum-radius will be different, and hence, the area of the circum-circle will also be different.
Also, in GMAT, the term circum-center won't really be used. It would be better to define what a circum-center is. Even then, this seems a bit out of scope of GMAT.
30 Jan 2020, 00:47
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=>
Since point \(O\) is the circumcenter of triangle \(ABC, OA = OB = OC\) is the radius of the circumscribed circle of the triangle.
Since the perimeter of the triangle \(ABC\) is \(19\), we have \(OA + OC + 7 = 19, OA + OA + 7 = 19, 2(OA) + 7 = 19, 2(OA) = 12,\) or the radius \(OA = 6.\)
Thus, the area of the circumscribed circle of the triangle is \((62)π = 36π.\)
Therefore, the answer is D.
Answer: D
Since point \(O\) is the circumcenter of triangle \(ABC, OA = OB = OC\) is the radius of the circumscribed circle of the triangle.
Since the perimeter of the triangle \(ABC\) is \(19\), we have \(OA + OC + 7 = 19, OA + OA + 7 = 19, 2(OA) + 7 = 19, 2(OA) = 12,\) or the radius \(OA = 6.\)
Thus, the area of the circumscribed circle of the triangle is \((62)π = 36π.\)
Therefore, the answer is D.
Answer: D
