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Here is my full design file:
:point126425.

Other approaches, comments and solutions are always appreciated.

Acorn

Here is a detailed Hint about Angle Bisectors.


Clone the Triangle and move it to a Guides Layer.
Make two further Clones of the Triangle.
Ctrl+Rotate both about a vertex until you snap an...

ernie, thank you, your video is very clear and I appreciate you taking the time to make it.

When I approach the intersection, I get the magnet pointer appearing when I am near or on the...

ernie, I have no problem with Xara snapping circle centres, I simply cannot snap a line end (edit handle) to the crossing point of two circles and I cannot rotate a line exactly onto the same point....

Sorry Larry, was it not clear that the circle doesn't yet exist? You have to make it.

The top left edge has an overlap with the circle and the bottom has a gap.
The Area is a little under at...

ernie, thank you. This is the classical compass and ruler solution.

You are creating the angle bisector of the three vertices (only two are needed) to cross at the incircle position.
A circle...

The Challenge is to use Xara accurately and create the Inclicle of the presented Challenge Triangle.

126393

The Incircle is simply the largest one you can fit inside a given triangle.
The...