Question

in circle d, \\( \angle edh \cong \angle edg \\).
what is the length of \\( \overline{jg} \\)?
4 units
5 units
6 units
9 units

Explanation:

Step1: Use the property of congruent angles in a circle

Since \(\angle EDH\cong\angle EDG\) and \(DE = DE\) (common side), \(DJ\perp EG\) (a line from the center of a circle that bisects an angle formed by two chords will be perpendicular to the chord if the chords are congruent - here the chords \(EH\) and \(EG\) are related by the congruent angles). In right - triangle \(DJE\) and \(DJG\), we can use the property that if two angles of a triangle are congruent and the side is common, then the triangles are congruent. Also, we know that in a circle, if \(\angle EDH\cong\angle EDG\), then the chords \(EH\) and \(EG\) are related. But more simply, since \(EJ = JG\) (by the property of angles and chords in a circle: if a central - angle bisector is drawn, it bisects the chord). Given \(EJ = 4\) units.

Answer:

4 units