Answered

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do you agree that if two lines intersects at the center of a circle , then the two pairs of congruent arcs

Sagot :

Yes.

Two lines that intersect at the center of the circle formed two pairs of vertical angles.  By definition (Vertical Angle Theorem), vertical angles are congruent.

If the common vertex of these vertical angles is the center of the circle, therefore they are also central angles, and the arcs they intercept are congruent.