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avatar+1230 

A circle has a radius of $15.$  Let $\overline{AB}$ be a chord of the circle, such that $AB = 5$.  What is the distance between the chord and the center of the circle?

 Dec 20, 2023
 #1
avatar+129690 
+1

Ket the center of the  circle =  O

 

Draw a line  from  the center perpendicular to the  chord.. call this OM...this will bisect the chord

 

OA =  15

AM =  AB / 2 = 5/2 = 2.5

OM  = what we are looking for

 

Triangle AOM is right with AMO = 90°

 

So....by the Pythagorean Theorem

 

OM =  sqrt [ OA^2 -AM^2]  =  sqrt [ 15^2 - 2.5^2 ]  =  sqrt (875 / 4) = (5/2)sqrt (35) ≈ 14.79

 

cool cool cool

 Dec 20, 2023

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