In a circle, the distance from a chord of length 12 units to the midpoint of its minor arc is 4 units. What is the radius of the circle?

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Answer 1 · 2018-06-26T10:29:20

#color(blue)("Radius"=13/2)#

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Using diagram:

We are given:

#AB=12#

#CD=4#

Note that the midpoint of the arc #hat(ACB)# is also the midpoint of #AB#

#:.#

#AD=DB=1/2(AB)=6#

If we extend #CD# through the centre to #E#, we form the chord #CE#.

We now have two intersecting chords:

By the intersecting chords theorem:

#ADxxDB=CDxxDE#

#:.#

#6xx6=4xxDE#

#DE=36/4=9#

Diameter

#CE = DE+CD#

# \ \ \ \ \ \ 9+4=13 #

#"Radius"=(CE)/2=13/2#