$\underline{\text { Folklore }}$

Two isosceles triangles have equal bases and radii of their circumscribed circles. Must these triangles be equal?

#
Counterexample see figure: isosceles triangles $A B C$ and $D B C$ with a common base $B C$, inscribed in the same circle, are not equal.

![](https://cdn.mathpix.com/cropped/2024_05_06_34fd2032e75750f56a92g-21.jpg?height=378&width=343&top_left_y=71&top_left_x=869)

## Answer

Not necessarily.