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Selina Solutions Class 9 Mathematics Solutions for Exercise 17(A) in Chapter 17 - Chapter 17- Circles
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A chord of length 24 cm is at a distance of 5 cm from the center of the circle. Find the length of the chord of the same circle which is at a distance of 12 cm from the center.
Answer:
Let AB be the chord of length 24 cm and O be the center of the circle.
Let OC be the perpendicular drawn from O to AB.
We know, that the perpendicular to a chord, from the center of a circle, bisects the chord.
AC = CB = 12 cm
Video transcript
"hello students welcome to leader q a
video session i am seth
your math tutor and the question for
today is a chord of length 24 centimeter
is at the distance of 5 centimeter from
the center of the circle
find the length of the pawn of the same
circle which is the distance of 12
centimeter from the center
now here from the question we know that
you can see the figure a b is the chord
which is at the distance of 5 centimeter
from the center row
so let a b be the cord
of 24 centimeter
which is at distance of 5 centimeter
from the o
so you have a b 24 centimeter
and you also have om
that is 5 centimeter
now om here is the perpendicular dropped
on the chord a b
you well know you are well known about
that that if you drop the perpendicular
from
center to the chord then this will
bisect the chord
so here perpendicular om
will bisect the cord
and hence you have a m
equal to mb and hence your
am will be equal to a b upon 2
it is 24 upon 2 and that is 12
centimeter that is your am
now consider right triangle amo in the
right triangle amo
you can apply the pythagoras property in
this triangle
that is am square plus om square
will be equal to ao square now here
first of all we need to find the radius
of the circle in order to find the
length of the second chord
that is cd so here the radius of the
circle will be
ao and that is according to the
pythagoras property
ao square is equal to am square plus om
square
hence your am is 12 centimeter that is
12 square
plus 5 square this is 169
that is ao square and hence your ao is
13
centimeter hence once you got the radius
now as a 13 centimeter you can proceed
further with the
calculation to find the length of the
remaining chord
so here consider the chord cd
now here there is a same scenario that
perpendicular
o n which is given
that is the distance from the center to
the
another chord that is 12 centimeter so
on is equal to 12 centimeter
now this divides the chord cd into two
equal halves
that is cn and nd
therefore c n is equal to n d
and hence we can find c n by the help of
pythagoras property
applying it to triangle ocn
in right triangle ocn so first of all
if you see the measurement of cn then we
need to find the cn
because here on is given that is 12
centimeter
and you have the radius now that is 13
centimeter so apply the pythagoras
property
in right triangle
ocn you have oc
square plus o n o c square
is equal to
o n square plus c n square
and hence your o n square here is 12
square the c n square is what you you
need to find
so 12 square minus oc square
will be equal to minus c n square
so there is a here oc that is you have
found that 13 square
minus 12 square that will be equal to cn
square
and that is exactly equal to 25
hence your cn comes out to be phi
now once you have found the cn you
already know
that cn will be equal to nd
so cd will be equal to cn plus nd
and which is 2 times cn
so here
hence you can say that
your called cd will be of measure 2
times
cn
and you already have the cn which is phi
that is 5 centimeter
so cd will be equal to
2 into 5 and that is 10 centimeter
hence our length of the required chord
that is the length of the new cord
will be equal to 10 centimeter
and this is our final answer so if you
have any query regarding this
you can drop it down in our comment
section and subscribe to lido for more
such interesting q a
thank you for watching"
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