SOLUTION: the center of a circle is at (-3,2) and its radius is 7. Find the length of the chord, which is bisected at (3, 1).

Question 1184227: the center of a circle is at (-3,2) and its radius is 7. Find the length of the chord, which is bisected at (3, 1).

Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52787) (Show Source): You can put this solution on YOUR website!
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the center of a circle is at (-3,2) and its radius is 7. Find the length of the chord, which is bisected at (3, 1).
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The distance between the given points is = . It is the length of the leg of the right angled triangle, whose hypotenuse is 7. THEREFORE, half of the chord's length is = = = . The entire chord is twice this length, or . ANSWER

Solved.

Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

the center of a circle is at (,) => and
and its radius is
equation is:

Find the length of the chord, which is bisected at (,)

if the chord is bisected at (,), find solutions for intersection of the circle with vertical line x=3

is the of the chord so angle is a angle.
Use coordinates (,) and (,) to find the length of the line segment .
Now you can use Pythagoras theorem to find the length of the line segment , which is the length of the chord.
=distance between points (,) and (,)

-> half the length of the chord
the length of the chord will be =>answer

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