rashmi Posted August 29, 2004 Share Posted August 29, 2004 C is a circle, L is a line, and p is a point on line L. If C,L and P are in the same plane and P is inside C, how many points do C and L have in common? a) 0 b) 1 c) 2 d) 3 e) 4 Quote Link to comment Share on other sites More sharing options...
arkham Posted August 29, 2004 Share Posted August 29, 2004 Is the answer 0? Quote Link to comment Share on other sites More sharing options...
jacob Posted August 29, 2004 Share Posted August 29, 2004 is it c) 2 ? since they are in the same plane Quote Link to comment Share on other sites More sharing options...
lanpapa Posted August 29, 2004 Share Posted August 29, 2004 i know this problem, the one in 10th ed. right? while i was doing the problem, i answered B. But after i checked the answer key, guess what, it is C. could someone tell me why? maybe someone would be nice to draw it perhaps? Quote Link to comment Share on other sites More sharing options...
dmitts Posted August 30, 2004 Share Posted August 30, 2004 hi... ya i think the answer ought to be C ie 2. Since the circle and line are in the same plane, there are two possibilities when a circle and line intersect. One is that the line is a tangent, in which case there will only be one pt common with the two. The other one is that the line intersects the circle in two points. In this prob since it is given that the line L has a point P which lies inside the circle C( read here..pt is not ON the circle but IN it), so the line must not be a tangent and hence intersects it in 2 points- ptA and ptB as i've drawn in the figure hope this explains it Dmittsprob.bmp Quote Link to comment Share on other sites More sharing options...
bigduke Posted August 31, 2004 Share Posted August 31, 2004 the rule / theorem, "a line that shares 2 points with a circle is called a secant" comes to mind :D Quote Link to comment Share on other sites More sharing options...
Welyse Posted August 31, 2010 Share Posted August 31, 2010 what if the line is stop at some points within the circle? P can still be inside of C and there is only 1 common? http://www.flickr.com/photos/46761656@N06/4945334873/ Quote Link to comment Share on other sites More sharing options...
paul2432 Posted August 31, 2010 Share Posted August 31, 2010 what if the line is stop at some points within the circle? P can still be inside of C and there is only 1 common? If the line stops, then it is a ray (stops at one end) or a line segment (stops at both ends). A line, by definition, extends infinitely in both directions. Paul Quote Link to comment Share on other sites More sharing options...
Welyse Posted August 31, 2010 Share Posted August 31, 2010 Thank you :) Quote Link to comment Share on other sites More sharing options...
BuzzLiteBeer Posted September 1, 2010 Share Posted September 1, 2010 I thought this was gonna be a trick question based on the title. Guess not. Quote Link to comment Share on other sites More sharing options...
Skychild Posted September 4, 2010 Share Posted September 4, 2010 Good question and nice explanation from dmitts. Quote Link to comment Share on other sites More sharing options...
Recommended Posts
Join the conversation
You can post now and register later. If you have an account, sign in now to post with your account.