In a circle a chord 12 cm long is parallel to a tangent and bisects the radius drawn to the point of tangency.

Question

Your supposed to find how long the raduis is. I tried drawing it out but I am still not getting it, I don't get how you can find the radius when your only given 1 number.

Answer 1

r^2 =(r/2)^2 +6^2
4r^2 =r^2 +36*4
3r^2 =3*12*4
r^2 =48
r=4√3 cm

Answer 2

The fact that the chord is parallel to a tangent and bisects a radius means that the chord is perpendicular to the radius it bisects. The chord is also bisected by the radius. Each of the two half chords defines a number of right triangles with a leg of length 6cm and a leg of length ½r. If you consider a version of this circle centered at the origin with bisected radius oriented along the x-axis (in the positive direction), then the points of the vertices of one of those triangles can be listed as: A = (0, 0), B = (½r, 0), and C = (½r, 6).

The segments AB and BC are legs of their right triangle, and AC is the hypotenuse.

Let h represent the length of AC. Thus,

h² = (½r - 0)² + (6 - 0)²
h² = ¼r² + 36

Since segment AC is also a radius,

h² = r²

Hence,

¼r² + 36 = r²
36 = ¾r²
48 = r²
√48 = r
4√3 = r

Answer 3

OK... I am not a Math Major, but I believe there is a way to find the length of a chord, if you know the radius and central angle (and you can figure out the central angle from your question... I'm guessing the angle is 90 degrees, since tangents are 90 degrees to the radius, and the chord is parallel to the tangent, yes?).. ok... here is the formula...

Chord Length= 2r sin (c/2) c--subtended angle to center by chord (i'm guessing 90, but you'd probably know better),

So... C is going to be the angle formed at the center by the bisection of the chord and radius....
I'm guessing, I havent' worked it out, but if you know the chord length and angle, you can flip the equation around and solve for the radius, right?
Again.. I have a degree in English; but I kinda remembered this stuff from the College Math I had to repeat three times. :)
Good luck.

Answer 4

Draw the lines and you'll see a right triangle with legs r/2 and 12/2.
http://i233.photobucket.com/albums/ee195/DWRead/swimbunny107.jpg

The hypotenuse is a radius, so the Pythagoerean theorem applies.
r² = 6² + (r/2)²
r² - r²/4 = 36
(3/4)r² = 36
r² = 36/(3/4)
r² = 48
r = 4√3

Answer 5

You have a right triangle with hypotenuse = r, one leg = 12/2 = 6 and the other leg = r/2.
Thus r^2 = r^2/4 +6^2
3r^2/4 = 36
3r^2 = 144
r = 12/sqrt(3) = 4sqrt(3)

Answer 6

12 To Cm

Answer 7

Circle:

x^2+y^2 = r^2

Tangent (point of tangency (r,0)):

x = r

Chord:

x = r/2

End points of the chord:

(r/2)^2 + y^2 = r^2 => y = +/-sqrt(3) r /2

Long of the chord:

sqrt(3) r = L

Then,

r = L/sqrt(3) = 6.9282 cm

Answer 8

i think u r going in circles
try again