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Schools: HBS(08) - Ding. HBS, Stanford, Kellogg, Tuck, Stern, all dings. Yale - Withdrew App. Emory Executive -- Accepted, Matriculated, Withdrewed (yes, I spelled it wrong on purpose). ROSS -- GO BLUE 2011.
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
Circle can intersect triangle at one of the vertices - 1 point of intersection; Circle can intersect triangle at two of the vertices - 2 points of intersection; Circle can intersect triangle at three of the vertices (inscribed triangle or inscribed circle) - 3 points of intersection; Circle can intersect triangle at two of the vertices and two sides - 4 points of intersection; Circle can intersect triangle at one of the vertex and cut three sides (one side twice and other two once) two sides - 5 points of intersection; Circle can cut all three sides twice - 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).
Below is the diagram showing possible cases of intersections provided by DestinyChild.
TriangleCircleIntersection88639.jpg [ 5.38 KiB | Viewed 55053 times ]
Re: No clue for this DS question - from gmatprep [#permalink]
03 Sep 2010, 02:58
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Imagine a triangle ABC. And draw a circle around it. 1 point - Just one side of the triangle is tangential to the circle. 2 pts - The circle is encompassing only one vertex. So it cuts at 2 points. 3 pts - A incircle. A circle where all the sides are tangents to it. Like we have in a in-circle 4pts - Draw a circle which passes through vertex A (pt1), cuts side AB (pt2), is tangential to BC (pt3) and finally cuts side AC (pt4). 5 pts - Gets trickier. Draw a circle which passes through vertex A (pt1), Cuts side AB (pt2), cuts side BC twice (pt3, pt4), and finally cuts side AC (pt5). 6 pts - this is the simplest. Draw a circle which cuts each side twice.
Hand me a kudos if you like my explanation. Thank you. -pH
Which of the following lists the number of points at which a [#permalink]
28 Sep 2015, 07:14
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Absolute Values/Modules tag is not required for this .
When everything seems to be going against you, remember that the airplane takes off against the wind, not with it. - Henry Ford The Moment You Think About Giving Up, Think Of The Reason Why You Held On So Long +1 Kudos if you find this post helpful
Last edited by Skywalker18 on 28 Sep 2015, 07:16, edited 1 time in total.
As per wikipedia..
"In plane geometry, a line is tangent to a curve, at some point, if both line and curve pass through the point with the same direction. Such a line is called the tangent line (or tangent)......It is a mistake to think of tangents as lines which intersect a curve at only one single point. ....
Note that in the important case of a conic section, such as a circle, the tangent line will intersect the curve at only one point..."
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