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The circle touching or passing through three things you click.

Menu: Construct > Circle: Apollonius | Node: Circle: Apollonius | In depth: Circles & arcs

Click three things for the circle to touch or pass through: a point, circle, arc, line, segment or ray. A point is passed through, everything else is touched. Clicking the same object twice is refused, so each of the three picks has to be a different object.

You can also select first. Pick up to three objects before running the command and they become the tool's picks instead of being discarded. Select fewer than three and it asks for the rest. Select exactly three and it goes straight to the ghost preview, or tells you at once that nothing fits. It never finishes on its own, because which of the answers to keep is decided by where your cursor is.

After the third pick a ghost preview appears and the cursor chooses among the answers. There is usually more than one circle that fits, so move the cursor until the one you want is showing and click to keep it. This mirrors the way the Line: Tangent to Circle line tool picks its side.

If nothing can meet all three, Locus says so on the third click rather than leaving you hunting a ghost that will never appear.

The circle it creates is a real construction object, derived from the three things you picked. Move any of them and it re-solves, keeping the same solution: the same contacts, on the same side, and the same size among any answers that share both. The circle you keep is the ghost you were looking at when you clicked. It does not jump to whatever now happens to sit at that position in the list of answers.

Circles saved before this change keep resolving the old way.

If the chosen solution stops existing, the circle goes unresolved, the same way a circumcircle through three points does when they fall in a line. Move the objects back and it comes back.

Deleting any of the three objects deletes the tangent circle with it.

< Previous: Tangent to Two Circles | Next: Circle Tangent to... >

• In the node graph: Circle: Apollonius builds the same circle as a node, and returns every solution as a collection rather than asking you to pick one.
• Line: Tangent to Circle: the tangent line from a point to a circle.
• Circles & arcs | Construct menu