# Thread: seems easy , yet !!!!

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## seems easy , yet !!!!

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

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## Re: seems easy , yet !!!!

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## Re: seems easy , yet !!!!

is it c) 2 ? since they are in the same plane

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## Re: seems easy , yet !!!!

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?

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## Re: seems easy , yet !!!!

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

Dmitts

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## Re: seems easy , yet !!!!

the rule / theorem, "a line that shares 2 points with a circle is called a secant" comes to mind

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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?

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Originally Posted by Welyse
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

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Thank you

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I thought this was gonna be a trick question based on the title. Guess not.