iran-konkur 2019 Q126

iran-konkur · Other · konkur-riazi_1398_specialized_new-curriculum Circles Inscribed/Circumscribed Circle Computations
126. An isosceles trapezoid, under which condition can be inscribed in a circle?
  1. [(1)] Two diameters perpendicular to each other
  2. [(2)] One of the bases of the trapezoid equals one of the legs
  3. [(3)] The line connecting the midpoints of the two legs passes through the intersection of the diameters
  4. [(4)] The length of the segment connecting the midpoints of the two legs equals one of the legs

\textbf{126.} An isosceles trapezoid, under which condition can be inscribed in a circle?

\begin{enumerate}
\item[(1)] Two diameters perpendicular to each other
\item[(2)] One of the bases of the trapezoid equals one of the legs
\item[(3)] The line connecting the midpoints of the two legs passes through the intersection of the diameters
\item[(4)] The length of the segment connecting the midpoints of the two legs equals one of the legs
\end{enumerate}

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