SOLUTION: A circle has radius 5 and centre (2, 4). The point (3,2) is the midpoint of a chord of this circle. Find the distance of the chord from the centre and the length of the chord.

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Question 1195534: A circle has radius 5 and centre (2, 4). The point (3,2) is the midpoint of a chord of this circle. Find the distance of the chord from the centre and the length of the chord.
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
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if the point (3,2) is the midpoint of a chord and centre (2,+4), the distance of the chord from the centre is equal to the distance between centre (2, 4) and the point (3,2)
d=sqrt%28%283-2%29%5E2%2B%282-4%29%5E2%29
d=sqrt%281%2B4%29
d=sqrt%285%29
the distance of the chord from the centre is sqrt%285%29


the length of the chord:
midpoint of the chord, center and endpoint of the chord for right triangle
one leg is d=sqrt%285%29, hypotenuse is radius r=5, and other leg is a half the length of the chord
so, let the length of the chord be c
then c=sqrt%28r%5E2-d%5E2%29
c=sqrt%285%5E2-sqrt%285%29%5E2%29
c=sqrt%2825-5%29
c=sqrt%2820%29
c=sqrt%284%2A5%29
c=2sqrt%285%29
the length of the chord is 2sqrt%285%29

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
A circle has radius 5 and centre (2, 4). The point (3,2) is the midpoint of a chord of this circle. Find the distance of the chord from the centre and the length of the chord.
Two of the circle's radii and the chord form an isosceles triangle

The distance the chord is from the circle's center is also this isosceles triangle's height, and is: 

The isosceles triangle's height creates 2 congruent right-Δs, with each having congruent basea that're 

The bases of both right triangles form the chord. Therefore, length of the chord =