How to Construct a Circle to Two Tangents
You can construct a circle from two non-parallel lines such that the circle fits snugly against the lines--in other words, so the lines are tangent to the circle. Such a problem may come up in a geometry class to practice shape construction. You can solve the problem with a straightedge and compass, algebraically or using calculus. Using a straightedge and compass, though not the most exact approach, is the fastest.
Other People Are Reading
Instructions
-
-
1
Denote the two lines to be made tangent to the circle as Lines 1 and 2.
-
2
Draw a line perpendicular to Line 1. Draw it through Line 1 at any point except where Line 1 and 2 intersect. Extend this line to intersect Line 2 as well. Denote the segment of this line between Lines 1 and 2 by the letter S.
-
-
3
Measure where the middle of the segment S is and mark it.
-
4
Draw a line perpendicular to Line 2 through the midpoint of S.
-
5
Denote the segment perpendicular to Line 1 and running from Line 1 to the midpoint of S by S1.
-
6
Denote the segment perpendicular to Line 2 and running from Line 2 to the midpoint of S by S2.
-
7
Denote the midpoint of S with the letter C, for “center,” since this is the center of the circle you’ll create.
-
8
Use the compass to construct a circle with center at C and radius of length S1 and S2, which are of equal length. Since S1 and S2 are perpendicular to Line 1 and 2, the circle constructed from them is tangent to Line 1 and Line 2.
-
1
Tips & Warnings
Another construction is to locate the point P where the two lines intersect and construct a third line through P that bisects the angle at P between Line 1 and 2. Draw a line perpendicular to Line 1 through the third line at point C and measure the distance D along it from Line 1 to the third line. D will be the radius of the circle you'll construct. Use a compass to construct a circle of radius D centered at point C.
References
- Photo Credit drawing equipment image by Christopher Hall from Fotolia.com
