Question 1085057
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<pre>
Three segments make a right-angled triangle:

1)  the half of the chord;

2)  the perpendicular bisector from the center of the circle to the chord;  and

3)  the radius drawn from the center to the chord's endpoint.


The half of the chord has the length of {{{8/2}}} = 4 units.

The perpendicular bisector from the center of the circle to the chord has the length

    {{{sqrt((2-(-1))^2 + (3-4)^2)}}} = {{{sqrt(3^2 + (-1)^2)}}} = {{{sqrt(10)}}}.

So, the right-angled triangle has two legs of 4 units and {{{sqrt(10)}}} units long.


The radius of the circle is the hypotenuse of this triangle.

Hence, its length is {{{sqrt(4^2 + (sqrt(10))^2)}}} = {{{sqrt(16 + 10)}}} = {{{sqrt(26)}}}.
</pre>

<U>Answer</U>. &nbsp;The radius of the circle is &nbsp;{{{sqrt(26)}}}&nbsp; units long.


Solved.