What equality must be satisfied so that a circle can be inscribed in a convex quadrilateral ABCD?
| August 31, 2021 | education
We will use the following theorem. In order for a circle to be inscribed into a convex quadrilateral, it is necessary and sufficient that the sum of the lengths of the opposite sides be equal to each other.
If a convex quadrilateral ABCD is given, then, obviously, its side AB the opposite side will be the side CD, similarly, side AD the opposite side will be the side BC. Based on the theorem given in item 1, the answer to the question posed in the problem is AB + CD = BC + AD.
Answer: AB + CD = BC + AD.
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