SOLUTION: Is there a formula to answer the following question? I know the chord of a circle is 10" and at the mid point of this chord is another line that reaches up to the edge of the cir

Is there a formula to answer the following 
question? 
I know the chord of a circle is 10" and at 
the mid point of this chord is another line 
that reaches up to the edge of the circle and 
it is 1" long. What is the radius of the
circle? this question is not in a text book. 
Thank you for your time, 
Amy


Draw a circle with center O. 
Draw the chord AB
Let C be the midpoint of AB
Draw radius OA
Draw OC
Extend OC until it intersects the circle at D.
You are given CD = 1 and that AB = 10", so AC = 5"

Let the radius be r.

Then OD = r for it is a radius
You are given that CD = 1
So OC = OD - CD = r - 1
OA = r for it is a radius

Now use the Pythagoean theorem on
right triangle OAC

OC² + AC² = OA²

or

(r - 1)² + 5² = r²
(r - 1)² + 25 = r²

Can you solve that?  If not post again
asking how.

r = 13 or the radius is 13"

Edwin