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goldphenoix · Answer

What do you need help with?

anonymous · Answer

The diameter AC of circle O is 24 cm. Triangle COD is equilateral. Arcs AB and CD are congruent. Use this information, the diagram, and your experiences in geometry this semester to answer these questions. (Use pi)
 a.)	What is the length AB?
b.)	What are the measures of angles ACB and BAC?
c.)	What is the sine of angle BAC?
d.)	Find the length of arc AB to the nearest hundredth.
e.)	How does the length of arc BC compare to the length of arc AB?

anonymous · Answer

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anonymous · Answer

a) since arcs AB and CD are congruent, the lengths of the shords connecting the points must  also have equal measure. So, AB = 12cm

b)|dw:1369941012729:dw|
angle ACB = sine inverse of 12/24 = 30 degrees.

c)sine of angle BAC = sin(90 - BAC) = cos( BAC) = sqrt(3)/2

d) length of arc = 60/360 ( 2 * 3.14 * 12 ) = 12.56 cm

e)length of arc BC = 1/2 circumference - length of arc AB
    = 1/2( 2 * 3.14 * 12) - 12.56 cm = 37.68 - 12.56 cm = 25.12 cm