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26 Jun 2007, 03:18
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E
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Which of the following lists the number of points at which a circle can intersect a triangle?
A. 2 and 6 only
B. 2, 4 and 6 only
C. 1, 2, 3 and 6 only
D. 1, 2, 3, 4 and 6 only
E. 1, 2, 3, 4, 5 and 6 only
A. 2 and 6 only
B. 2, 4 and 6 only
C. 1, 2, 3 and 6 only
D. 1, 2, 3, 4 and 6 only
E. 1, 2, 3, 4, 5 and 6 only
17 Mar 2009, 07:53
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Accountant
This is understanding how geomoetric figures work.
The options are 1,2,3,4,5,6
points that interesect.
I made a nice picture that shows all six options, so the answer is E.
Attachments
circles.JPG [ 8.8 KiB | Viewed 200048 times ]
22 Feb 2010, 11:28
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Which of the following lists a number of points at which a circle intersects a triangle
A. 2 and 6 only
B. 2, 4 and 6 only
C. 1, 2, 3 and 6 only
D. 1, 2, 3, 4 and 6 only
E. 1, 2, 3, 4, 5 and 6 only
A circle can intersect a triangle at:
Hence circle can intersect triangle at 1, 2, 3, 4, 5 or 6 points. (The examples I provided are not the only possible cases of intersection points, just these examples prove that there can be from 1 to 6 intersections).
Answer: E.
Below is the diagram showing possible cases of intersections provided by DestinyChild.
TriangleCircleIntersection88639.jpg [ 5.38 KiB | Viewed 210526 times ]
A. 2 and 6 only
B. 2, 4 and 6 only
C. 1, 2, 3 and 6 only
D. 1, 2, 3, 4 and 6 only
E. 1, 2, 3, 4, 5 and 6 only
A circle can intersect a triangle at:
- 1. One of the vertices, resulting in 1 point of intersection.
2. Two of the triangle's vertices, giving 2 points of intersection.
3. All three vertices (as in the case of an inscribed triangle or circle), leading to 3 points of intersection.
4. Two vertices and two sides, creating 4 points of intersection.
5. One vertex and cut across three sides (intersecting one side twice and the other two sides once), totaling 5 points of intersection.
6. The circle can intersect all three sides twice, resulting in 6 points of intersection.
Hence circle can intersect triangle at 1, 2, 3, 4, 5 or 6 points. (The examples I provided are not the only possible cases of intersection points, just these examples prove that there can be from 1 to 6 intersections).
Answer: E.
Below is the diagram showing possible cases of intersections provided by DestinyChild.
Attachment:
TriangleCircleIntersection88639.jpg [ 5.38 KiB | Viewed 210526 times ]
