Question

Asked Mar 23, 2019

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Proposition: Let e be an edge of a triangulation, where e = AC belongs to the two triangles ABC and ACD. Then e is a legal edge if D is outside the curcumcircle of ABC and and illegal edge if D is inside the circumcircle.

Question: Given the triangles defined proposition, show that D is outside the circumcircle of ABC if and only if B is outside the circumcircle of ACD, **prove this is true even if ABCD does not form a convex quadrilateral. **

(Attached is an image of the convex quadrilateral.)

Step 1

To prove that D is located outside the circumcircel of the triangle ABC, under the given conditions

Step 2

Step 3

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