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Question 248158: What is the locus of the midpoints of all chords of length 4 in a given circle with radius of length 3?
Answer by vleith(2983)   (Show Source):
You can put this solution on YOUR website! Imagine a chord of length 4 inside a circle with radius 3.
Now draw lines from the two chord endpoints to the center of the circle.
You see that you have an isosceles triangle.
Draw in the radius that intersects the chord midpoint.
Now you have two triangles, each is a right triangle with a hypotenuse of 3 and one side of 2.
Use the Pythagorean theorem to solve for the third side. <-- keep this value
Now imagine "sliding" that chord around inside the circle. What pattern does the midpoint make?
So there you have it, You have a circle around the same center, but with radius of the length you solved for above.
Get it?
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