Math question to do with geometry?

Question

A circle has a radius of 8. A chord of this circle is the perpedicular bisector of a radius. The length of the chord is

I know the answer is 8
But for the life of me I cant explain why
Somebody want to help me with "bisector of a radius"

Answer 1

The answer is not 8. Instead, it's 8 sqrt(3). Here's why ...

Since the chord is the perpendicular bisector of the radius, (a) it cuts the radius in half (each half of the radius is 4); and (b) it forms a right angle with the radius.

Draw this diagram: First, a circle with radius 8 with center at O. Draw a radius OA. Draw the chord that perpendicularly bisects the radius. Label the ends of the chord (where it cuts the circle) as B and C. Let point D be where the radius and chord intersect. (There are right angles at D.) Finally, draw a radius from O to B.

Triangle ODB is a right triangle. That's what we're going to work on. OB (the hypoteneuse) is 8 because it's a radius of the circle. OD is 4 because it's half your original radius. And BD (the third side of the right triangle) is half the chord you're looking for.

By the Pythagorean theorem,

BD^2 + OD^2 = OB^2
BD^2 + 4^2 = 8^2
BD^2 + 16 = 64
BD^2 = 64 - 16 = 48 = 16*3
BD = sqrt(16*3) = 4 sqrt(3)

But BD is only half your chord, so the full chord is

BC = 2 BD = 8 sqrt(3)

That's your answer, and that's how to do it.

Answer 2

Once you draw the chord and the radius to which it is the perpendicular bisector, connect the end points of the chord to the center of the circle. Notice that you now have 2 right triangles. Just consider one of them. The hypotenuse is the radius which is 8, the other side is 4 since it is half of the radius and you can find the third side by the pythagoreous theoram. Double it and you get the length of the chord. Hope that helps!

Answer 3

The radius bisects the chord.
Each part from the center will be 8/2=4
Join the center and one end point of the chord.
It will be radius .
Use pisagor relation
x^2+4^2=8^2
x^2=64-16=48
x=4 sqrt(3)

the length of the chord is 2x
=8sqrt(3)

Answer 4

radius is the line joining centre and a point on circle periphery
its perpendicular bisector is through it's midpoint and extending between two points on the periphery
the line joining the centre and one end point of chord is also a radius
so ur required length of chord is twice the sqrt(8^2-(8/2)^2) i.e.13.8564 or 13.9

Answer 5

radius of the circle=8
half of the chord=(64-16)^1/2
so the length of the chord=2(4rt3)
=8rt3 or 8*1.732=13.9

Answer 6

once i tried to tie a piece of string to a piece of pencil & decided to make a transition piece for a launch ramp (circa '89) so no, i have NO idea!. Have fun w/ that!