SOLUTION: find the radius of a circle with center at (2,3), if the chord of length 10 is bisected at (-3,0)

Question 1045494: find the radius of a circle with center at (2,3), if the chord of length 10 is bisected at (-3,0)
Found 6 solutions by josgarithmetic, ikleyn, advanced_Learner, blaser211, MathTherapy, Edwin McCravy:
Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
I have not thought all the way through this yet nor done any calculations, but, do this: Find the equation of the line which contains the chord.
Answer by ikleyn(52802)   (Show Source): You can put this solution on YOUR website!
.
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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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 = = = units. Its leg AB has the length = 5 units. Hence, the hypotenuse OA has the length = = . The hypotenuse OA is the radius of the circle. Hence, the radius is units long. Answer. The radius is units long.

On properties of chords in a circle see the lessons
    - A circle, its chords, tangent and secant lines - the major definitions
    - The longer is the chord the larger its central angle is
    - The chords of a circle and the radii perpendicular to the chords
in this site.

In this site, you have free of charge systematic and logically organized online textbook in Geometry
    - GEOMETRY - YOUR ONLINE TEXTBOOK.

Answer by advanced_Learner(501)   (Show Source): You can put this solution on YOUR website!
the radius is the distance from the centre to the point of interection
=
=
equation is
=
graph confirms
.

Answer by blaser211(6)   (Show Source): You can put this solution on YOUR website!
sorry i in put the wrong problem...
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
find the radius of a circle with center at (2,3), if the chord of length 10 is bisected at (-3,0)

Length of perpendicular bisector from the center to the chord (one leg of right triangle with central angle as one of the vertices):
Length of other leg of right triangle, with a value that is : 5 units
Length of radius (r), or hypotenuse of right triangle:
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!

Edwin

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