Tangent Circles to Two Parallel Lines and Passing through a Point

slope

m

1.2

y intercepts

b

1

2.1

b

2

5

coordinates of red point

x

7.8

y

13.7

This Demonstration is based on an example from a Wolfram Education Group seminar: Given two parallel lines and a point

P

between them, draw circles of radius

r

centered at

Q

1

and

Q

2

through

P

and tangent to the lines. Then the circle centered at

P

with radius

r

passes through

Q

1

and

Q

2

.

Here we allow the two blue circles to be constructed when the point is not between the two lines.

Details

The distance from a point

(u,v)

in the

x

-

y

plane to the line with equation

y=mx+b

, where

m

is the slope of the line and

b

is the

y

intercept, can be proven to be

mu+b-v

2

m

+1

.

See the Wolfram Education Group seminar, Calculus: Fundamentals.

External Links

Tangent Circles (Wolfram MathWorld)

Point-Line Distance--2-Dimensional (Wolfram MathWorld)

Parallel Lines (Wolfram MathWorld)

Permanent Citation

Abraham Gadalla

"Tangent Circles to Two Parallel Lines and Passing through a Point"
http://demonstrations.wolfram.com/TangentCirclesToTwoParallelLinesAndPassingThroughAPoint/
Wolfram Demonstrations Project
Published: July 1, 2011