Question

in ( odot o, moverparen{ab}=50 ) and ( overline{ca} cong overline{bd} ).
what is ( moverparen{cd} )?
( moverparen{cd}=square )

Explanation:

Step1: Use the property of congruent chords

Since \(\overline{CA}\cong\overline{BD}\), then \(\overset{\frown}{CA}\cong\overset{\frown}{BD}\).

Step2: Analyze the relationship between arcs

We know that \(\overset{\frown}{AB}\) and \(\overset{\frown}{CD}\) are related. In a circle, if \(\overset{\frown}{CA}\cong\overset{\frown}{BD}\), then \(\overset{\frown}{AB}\cong\overset{\frown}{CD}\) (by the property that if we subtract the congruent arcs \(\overset{\frown}{CA}\) and \(\overset{\frown}{BD}\) from the whole - circle - related arc combinations).

Answer:

\(50\)