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)
Responses

11 mm
11 mm

10 mm
10 mm

20 mm
20 mm

7 mm
7 mm

Answer 1

KL and KM are tangents, so FL ⟂ KL and FM ⟂ KM. In right triangle KFL (right at L), angle K = 35°, KF = 12 is the hypotenuse and FL = MF is the side opposite that angle. Thus

MF = KF·sin(35°) = 12·sin35° ≈ 12·0.5736 ≈ 6.88 mm ≈ 7 mm.

Answer: 7 mm.