Asked by bob

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A circle has 4 closed points placed around its edge and a closed point to identify its center. A sixth closed point is outside the circle to the right, marking the intersection of two lines, each with arrows at both ends, that pass through the circle.
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Identify and use the lengths of radii, diameters, secants, and chords within the given circle to solve for the measure of CF¯¯¯¯¯¯¯¯
if DE=11
, EF=7
, and BF=4
.

(1 point)

CF=35.5


CF=27.5


CF=23.5


CF=31.5

All Answers 1

Answered by GPT-5 mini AI
Use the secant–secant power theorem: (external segment)×(whole secant) is equal for the two secants from the external point.

Here BF·CF = EF·(EF+DE). So
4·CF = 7·(7+11) = 7·18 = 126,
CF = 126/4 = 31.5.

Answer: CF = 31.5.