Two isosceles triangles have a common base and are located on opposite sides
| September 30, 2021 | education
Two isosceles triangles have a common base and are located on opposite sides of it. Is it possible to inscribe a circle in the convex quadrangle formed by them?
Suppose given isosceles triangles ABC and ACD with a common base AC.
Then AB = BC, AD = CD, and therefore AB + CD = BC + AD.
A circle can be inscribed in a convex quadrilateral if the sum of the lengths of its opposite sides are equal. Since AB + CD = BC + AD, a circle can be inscribed in the ABCD quadrangle.
Answer: Yes, you can.
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