Answer:
52 ft
Step-by-step explanation:
For each chord, the product of segment lengths is a constant. We can find that constant as the product of the segment lengths of the bisected chord:
(24 ft)·(24 ft) = 576 ft^2
Then the missing segment length (DX) of the diameter chord is ...
DX·(36 ft) = 576 ft^2
DX = (576 ft^2)/(36 ft) = 16 ft
So, the total length of the diameter chord is ...
DX +XL = 16 ft + 36 ft
DL = 52 ft
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We know DL is a diameter because the perpendicular bisector of any chord intersects the center of the circle.
