Question

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A circle has center point upper F. The circumference point upper L is at the left of the circle and the circumference point upper M is at the right of the circle. Point upper K is above the circle in line with upper F.
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If ∠L≅∠M
and both equal 90 degrees, ∠LKF=35
degrees, and KF=12
mm, then what is the length of MF
to the nearest millimeter?

(1 point)

7 mm

20 mm

10 mm

11 mm

Answer 1

KL and KM are tangents, so MF ⟂ KM. Thus triangle KFM is right with right angle at M and ∠MKF = 35°. With KF = 12 (hypotenuse),

FM = KF * sin(35°) = 12 * sin(35°) ≈ 12 * 0.5736 ≈ 6.88 mm ≈ 7 mm.

Answer: 7 mm.