Question 1045494
.
find the radius of a circle with center at (2,3), if the chord of length 10 is bisected at (-3,0)
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<pre>
Make a sketch. Let the point O = (2,3) be the center of the circle.
Let the point B = (-3,0) bisects the given chord.
Let A and C be endpoints of this chord.

Then the triangle OAB is a right-angled triangle.

Its leg OB has the length {{{sqrt((2-(-3))^2 + (3-0)^2)}}} = {{{sqrt(5^2 + 3^2)}}} = {{{sqrt(25+9)}}} = {{{sqrt(34)}}} units.

Its leg AB has the length {{{10/2}}} = 5 units.

Hence, the hypotenuse OA has the length {{{sqrt(34 + 5^2)}}} = {{{sqrt(34 + 25)}}} = {{{sqrt(59)}}}.

The hypotenuse OA is the radius of the circle.
Hence, the radius is {{{sqrt(59)}}} units long.

<U>Answer</U>.  The radius is {{{sqrt(59)}}} units long.
</pre>

On properties of chords in a circle see the lessons 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Circles/A-circle-its-chords-tangent-and-secant-lines-the-major-definitions.lesson>A circle, its chords, tangent and secant lines - the major definitions</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Circles/The-longer-is-the-chord-the-larger-its-central-angle-is.lesson>The longer is the chord the larger its central angle is</A> 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Circles/The-chords-in-a-circle-and-the-radii-perpendicular-to-the-chords.lesson>The chords of a circle and the radii perpendicular to the chords</A> 

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In this site, &nbsp;you have free of charge systematic and logically organized online textbook in Geometry 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson>GEOMETRY - YOUR ONLINE TEXTBOOK</A>.