SOLUTION: AB is a chord of a circle centre O. The radius of the circle is 50 cm long and the length of AB is 60 cm. What is the distance of AB from O?

Algebra ->  Circles -> SOLUTION: AB is a chord of a circle centre O. The radius of the circle is 50 cm long and the length of AB is 60 cm. What is the distance of AB from O?      Log On


   

Question 754364: AB is a chord of a circle centre O. The radius of the circle is 50 cm long and the length of AB is 60 cm. What is the distance of AB from O?
Found 3 solutions by dkppathak, Cromlix, Edwin McCravy:
Answer by dkppathak(439) About Me  (Show Source):
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length of chord is 60 cm
half of chord will be 30 cm (perpendicular from center to chord bisect the chord)
radius of circle is 50 cm
therefor it will be right triangle
whose hypotenuse will be 50 cm and other side half of chord 30 cm
distance of chord from center can be calculate by using Pythagoras theorem
H^2 = p^2 +s^2
p^2 =h^2-p^2
p^2 =50^2-30^2
P^2=2500-900
=1600
p= sqrt 1600
P =40 cm
ANSWER 40 cm

Answer by Cromlix(4381) About Me  (Show Source):
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A Pythagorean question.
Consider a line coming from centre O
and meeting the chord AB at its centre.
The chord would be divided into two pieces
each measuring 30cm.
Now if we swing a radius round to extend
from centre O to where AB touches the circumference
of the circle.
We now have a right angled triangle.
The radius is the hypotenuse, half of AB is the
base and the line from the centre to the chord
is the height.
By applying Pytagoras: the sum of the two sides
squared = the hypotenuse squared.
By adjusting the formula we find that if we take
the hypotenuse squared and take away from it,
the base squared, the answer when it is square
rooted = the distance from the centre O to the chord AB.
50^2 - 30^2 = the height^2
height^2 = 1600
height = 40 cm.
This is the distance from the centre O to the chord AB.
Hope this helps
:-)

Answer by Edwin McCravy(20060) About Me  (Show Source):
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Draw OC the perpendicular bisector of the chord, which
divides the 60 cm chord into two 30 cm line segments,
AC and BC.  We are looking for the length of OC:




Use the Pythagorean theorem on right triangle ACO

OAē = ACē + OCē
50ē = 30ē + OCē
2500 = 900 + OCē
1600 = OCē
√1600 = OC
40 = OC

Answer: 40 cm.

Edwin