Suppose two co-planar circles have no points in common. Dteremine how many lines, if any, are tangent to both circles.
2006-12-10 23:41:28 · 7 answers · asked by Sasha 2 in Science & Mathematics ➔ Mathematics
Picture a penny and a nickel on a table, not touching each other, and not too far apart, but less far apart than the length of a pencil.
That's two coplanar circles (the table is the plane). ANd no points in common if they don't overlap or touch.
Now, tangent lines touch the outsides of the circles. Pick four pencils and lay them along the coins so they touch both pennies. Don't worry if they touch each other.
It looks to me like you can lay them so that they cross between the two coins, forming an x, and that you can lay them outside the two coins, almost parallel (but because the coins are different sizes, they are not quite parallel).
So I think the answer is 4.
2006-12-10 23:50:15 · answer #1 · answered by firefly 6 · 0⤊ 0⤋
I think four is the correct answer. You would have two lines tangent to each circle which cross each other like an X between the circles, and another two lines, each of which lie on opposite sides of the crossing point of the first two lines, which are also tangent to the two circles.
2006-12-11 07:59:48 · answer #2 · answered by MathBioMajor 7 · 0⤊ 0⤋
I'm pretty sure it's infinately many. Because you can't see a single point on a circle, and if I'm correct, a line tangent to a circle only touches it in one point. So you can have many different lines going between the two cirlces. Too high to count any way.
2006-12-11 07:45:27 · answer #3 · answered by Toxxikation 3 · 0⤊ 3⤋
No points in common means on the circumdferences.
My guess is usually two.
However, suppose one circle is completely inside the other. They have no points in common, but they have no common tangents.
2006-12-11 07:48:10 · answer #4 · answered by fcas80 7 · 1⤊ 2⤋
You again? We all know this is not extra credit. We're tired of doing your homework for you. First, look up "tangent" in the dictionary, then draw 2 circles. You'll be able to figure it out unless you're a chimpanzee.
2006-12-11 08:31:35 · answer #5 · answered by Anonymous · 0⤊ 2⤋
In general there are 4.
(If one is inside the other then there are 0)
See:
http://mudandmuck.com/str2/circleTangents.jpg
2006-12-11 07:49:53 · answer #6 · answered by Scott R 6 · 3⤊ 0⤋
yea not a huge math expert soooo i can't really tell u this
2006-12-11 07:49:54 · answer #7 · answered by whitney s 2 · 0⤊ 3⤋