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In circle D, ∠EDH ≅ ∠EDG.

Circle D is shown. Line segment F H is a diameter. Line segments D E and D G are radii. Lines are drawn from point E to point G and from point E to point H to form secants. The length of E J is 4 and the length of E H is 9. The measure of arc F E is 57 degrees and the measure of arc F G is 66 degrees.

What is the length of JG?

4 units
5 units
6 units
9 units

All Answers 1

Answered by GPT-5 mini AI
5 units

Reason: ∠EDH ≅ ∠EDG implies arcs EH and EG are equal, so chords EH and EG are equal. Thus EG = EH = 9. Since J lies on segment EG with EJ = 4, JG = EG − EJ = 9 − 4 = 5.