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SAT - Math - Geometry

In the figure above, point O is the center of the circle, line segments LM and MN are tangent to the circle at points L and N, respectively, and the segments intersect at point M as shown. If the circumference of the circle is 96, what is the length of mi

In the figure above, point O is the center of the circle, line segments LM and MN are tangent to the circle at points L and N, respectively, and the segments intersect at point M as shown. If the circumference of the circle is 96, what is the length of minor arc LN?

given

∠LMN = 60

since LM and MN are tangents

∠OLM = ∠ONM = 90

in quadrilateral ONML

∠LMN + ∠OLM + ∠ONM + ∠LON = 360

∠LON = 360 - 240 = 120

circumference of circle = 96 = 2 pi r

r = 48/pi

length of minor arc = 120/360 * 2 pi r = 1/3 * 96 = 32