Circle Geometry?

Question

A circle with radius 89mm has a chord drawn 52mm from the centre.

How long is the chord to the nearest mm?

If you could explain how you got to the answer, thanks

Answer 1

If you draw the circle and the chord, and lines from the centre of the circle to the endpoints of the chord, and the line from the centre of the circle to the midpoint of the chord, this line will make a right angle with the chord.
This gives you a right-angled triangle with hypotenuse 89 mm, one minor side 52mm, and the other minor side half the length of the chord. Pythagoras' theorem then says that half the chord has length √(89^2 - 52^2) = √5217, so the chord has length 2√5217 = 144 mm to the nearest mm.

Answer 2

draw the circle with the chord.
from the center draw a line to and perpendicular to the chord.this line is 52mm.
draw another line from the center to one end of the chord forming a right triangle (this line is the hypotenuse=radius).

by pythagorean theorem: solve for half the length of the chord.
let
a = half of the chord
b = line from center of the circle to the center of the chord; 52mm
c = radius; 89mm

a^2 = 89^2 - 52^2 // you can solve it from here!
i hope this helps.

Answer 3

I hate geo.