question is from mathematics
2007-01-06 02:39:02 · 8 answers · asked by akshit 1 in Science & Mathematics ➔ Mathematics
Let me use (C1) and (C2) for the two different-sized circles with
centers C1 and C2. Draw the line l = C1C2, and the perpendiculars p1
and p2 to that line through C1 and C2 respectively.
The line p1 meets (C1) in two points P1 and Q1, and P2 and Q2 are
found on (C2) similarly.
The lines P1P2, Q1Q2, P1Q2, and P2Q1 intersect l in two points:
A and B. It is only useful to consider these points if they are
outside (C1) and (C2), as both will be when the two circles do not
intersect and are apart from each other; one of them will be outside
when one circle is not totally inside the other one.
A and B are the starting points for possible tangents to both circles.
If a tangent starts from, for instance, A, then the reflection of that
tangent through l is of course a tangent too, and thus two (or zero)
tangents start from one point.
Now you can construct the tangents from, for instance, A to (C1) in
the following way:
Draw the circle having AC1 as diameter, and find the intersection
points of this circle with (C1), say X1 and X2. The lines AX1 and AX2
are the two tangents we look for.
When two circles are do not intersect, you will find a total of four
common tangents to those circles.
2007-01-06 03:19:47 · answer #1 · answered by Mrswagger07 2 · 0⤊ 1⤋
Three if the circles touch at one point, four if they are disjoint (and one does not contain the other), and an infinite number if they are the same circle. If the circles share two points in common, however, you can only get two common tangent lines. If one contains the other completely you get no common tangent lines.
2007-01-06 11:14:43 · answer #2 · answered by Biznachos 4 · 1⤊ 0⤋
Imagine an angle formed by two lines. You can put really small circles near the angle tangent to both lines and you can put large circles far away from the angle touching both sides
2007-01-06 12:34:31 · answer #3 · answered by a_math_guy 5 · 0⤊ 0⤋
Yes, Four
2007-01-06 10:49:09 · answer #4 · answered by Sweet Dragon 5 · 2⤊ 0⤋
Yes, four. One touches them both on the top, the second touches them both on the bottom, and the third and fourth are criss-cross.
2007-01-06 10:46:04 · answer #5 · answered by bh8153 7 · 5⤊ 1⤋
You could have a third one if the circles were virtually touching.
2007-01-06 10:41:37 · answer #6 · answered by JJ 7 · 1⤊ 2⤋
Only if they are coincident. Then you can have infinitely many!
2007-01-06 10:42:15 · answer #7 · answered by Scarlet Manuka 7 · 0⤊ 2⤋
ya 4 are possible man!!!
2007-01-06 10:42:16 · answer #8 · answered by akshayrangasai 2 · 0⤊ 6⤋