SAT Mathematics Practice Test 2

Question : 56 of 58

Marks: +1, -0

In the figure above, point

O

is the center of the circle, line segments

L M

and

M N

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

L N

Your Answer:

Validate

Solution:

Since segments

L M

and

M N

are tangent to the circle at points

L

and

N

respectively, angles

O L M

and

O N M

are right angles. Thus, in quadrilateral

O L M N

, the measure of angle O is

360° − (90°+60°+90°)=120°.

Thus, in the circle, central angle O cuts off

120/360=1/3

of the circumference;that is,minor arc LN is

1/3

of the circumference.Since the circumference is 96,the length o f minor arc LN is

1/3×96=32

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