What is the radius of the arc?

Question

I want to know how to find the radius, not just the answer.

Thanks

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Answer 1 · 2018-01-27T14:57:41

Radius is #color(blue)(4.125)#

enter image source here

From the diagram:

Let the chord #AB=7.4# be the length of the given segment.

Let #CE=2.3color(white)(88)# be the distance from #AB# to the midpoint of the arc.

Let the diameter of the circle #CD=x#

If #CD# bisects #AB#:

Then:

#AE=3.7#

#EB=3.7#

And:

#ED=x-2.3#

By the theorem of intersecting chords:

#color(red)(AExxEB=CExxED)#

#:.#

#3.7xx3.7=2.3xx(x-2.3)#

#13.69=2.3x-5.29#

#18.98=2.3x#

#color(blue)(x=8.25)color(white)(8888888888888)# ( 2 .d.p.)

If #x# = the diameter #=8.25# , then radius is #x/2=color(blue)(4.125)#