Question

Circle K has a radius of 8 inches. Diameter AKC is drawn and point F is located on the circle such that
FC = 6. Which of the following is closest to the length of FA?

(1) 5.3
(2) 8.7
(3) 12.4
(4) 14.8

Answer 1

If Circle K has a radius of 8 inches. The figure that is closest to the length of FA is: 14.8.

Length

MAC=1/2×360°=180°

mΔAFC=1/2×180°=90°

Circumference angle theorem

AK=8

AC=2

AK=16

Pythagorean theorem

FA²+FC²=AC²

Substitution

FA²+6²=16²

FA²+36=256

FA²=√220

FA=14.8

Therefore the figure that is closest to the length of FA is: 14.8.

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