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.)

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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.)

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Expert Answer

Step 1

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

Step 2
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Step 3
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