Need help with chord length.

Christo133 · #1 $Old$ November 4th, 2009, 10:03 PM

I cannot for the life of me figure out a homework problem. My teacher is notorius for assigning stuff we haven't completely learned.

Need to know: Length of segment AB

Known information:

Each circle has a radius of 10cm. The centers all lie on line OE. Line OD intersects the middle circle and is tangent to the last circle.

I'm in trig, but I don't know if that's this problem. We haven't learned chords, secants or tangent lines but I know general info.

What I have figured out:

I drew a line done from the tangent point, I'm assuming that the angle off OE is the right triangle. The line down from point D is 10cm. Line OE is 50cm to the middle of the last circle. Angle O is arctan (10/50). I have no idea how any of this helps me though.

Thanks for sticking with it this far! :-)

bigwave · #2 $Old$ November 5th, 2009, 12:53 AM

the line from D to the center of the circle is perpendular to OD if OD is tangent to the circle.

if you have the length of 2 sides of right triangle

use the Pythagorian Theorm

in this case

$\sqrt {50^2 - 10^2} = lenght \ of \ OD\ \approxeq 48.98$

HallsofIvy · #3 $Old$ November 5th, 2009, 03:49 AM

Quote:

Originally Posted by Christo133 $View Post$

I cannot for the life of me figure out a homework problem. My teacher is notorius for assigning stuff we haven't completely learned.

Why would a teacher assign stuff you have completely learned, except as review? You learn by doing so your teacher is being completely reasonable.

Quote:

Need to know: Length of segment AB

Known information:

Each circle has a radius of 10cm. The centers all lie on line OE. Line OD intersects the middle circle and is tangent to the last circle.

I'm in trig, but I don't know if that's this problem. We haven't learned chords, secants or tangent lines but I know general info.

What I have figured out:

I drew a line done from the tangent point, I'm assuming that the angle off OE is the right triangle. The line down from point D is 10cm. Line OE is 50cm to the middle of the last circle. Angle O is arctan (10/50). I have no idea how any of this helps me though.

Thanks for sticking with it this far! :-)

Christo133 · #4 $Old$ November 5th, 2009, 08:08 AM

Thanks Big Wave, I got that far but I actually need line segment AB.

And HallsofIvy, he actually has never taught us tangent lines, secant lines, chord lines. Nor, does our Trig book cover them. Right now we are doing sum/difference formula, area of a triangle, etc. What I meant to say was, I can't figure out how to make any connection between the two. Trust me, I've tried.

bigwave · #5 $Old$ November 5th, 2009, 12:44 PM

to get the lenght of the chord AB

solve for the intersections of 2 equations
one for the line and the other for the circle
the intersections of the 2 equations
will give the endpoints of the chord AB
then use distance formula to find lenght
hope this helps...

i will do it later on if you need to see how this is done.... no time now.