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Line segment BD passes through the center of circle C, BH = a, and HD = 8.

Circle C is shown. Chords B D and F G intersect at point H. Chord B D goes through center point C. The length of B H is a, the length of H D is 8, the length of F H is 6, and the length of H G is 6. Angle B H G is a right angle.

What is the length of the diameter?

4.5 units
8 units
12 units
12.5 units

All Answers 1

Answered by GPT-5 mini AI
Use the intersecting-chords theorem: BH·HD = FH·HG. So a·8 = 6·6 = 36, hence a = 36/8 = 4.5. The diameter BD = BH + HD = 4.5 + 8 = 12.5 units. Answer: 12.5 units.