Creating a given radius circle, that passes through a point and is tangent to another circle.

[armaangohil]

I am trying to create a circle, whose radius is given to me. I want that circle to pass through, a point and should be tangent to another circle.

[RobDraw · Accepted solution]

You will need a third circle use the center of the circle you want to be tangent to with a radius equal to the distance of the point from the center. Draw the other circle tangent to the given circle anywhere. Then rotate it using the intersection of the circles that you want at the point.

Hope that makes sense.

[h_s_walker]

See the image below

[Washingtonn · Accepted solution]

Visual of what RobDraw said....

[armaangohil]

Thank for recreating the visuals. An easier introduction for a new learner like me to the software.

[armaangohil]

Thank you RobDraw for the solution.

[armaangohil]

Thanks for replying a different visualization to problem.

[armaangohil]

Only works if the radius(cr) = distance(point, outer circumference point of C) | Not a universal answer

[Washingtonn]

There is no universal answer  - you specified a circle of known radius to pass through a point and be tangent to an unknown circle.

  For points inside the unknown circle -> anywhere provided that the known circle radius is equal to 1/2 the radius of the unknown circle. A larger or smaller known circle radius will reduce available tangent point placements.

  For points outside the unknown circle -> locations no more than twice the radius of the known circle away from the perimeter of the unknown circle. The circle cannot pass through points located beyond that distance and still be tangent to the unknown circle.

[RobDraw]

Sure there are null solutions and a single radius that will hit the point only once but beyond that minimum, there are two possible solutions for every radius larger than the previously mentioned possibilities. 

In the context of this thread, the given solution is quite easily proven. 

[armaangohil]

Finally, I tried it again. With the help of geometry, I was able to create the circle.

Condition for the radius of the circle to be drawn is as specified by you.

Creating 2 locus:

Circle of radius to the drawn, should be created with given point as center for the circle.

Difference in radius, given circle and the circle to be drawn. Center of the given radius circle.

The intersection point gives us the center point for the circle to be created. We already know the radius, and hence create the circle.