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NCERT Exemplar Solutions Class 9 Mathematics Solutions for Circles - Exercise 10.2 in Chapter 10 - Circles
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Two chords AB and AC of a circle with centre O are on the opposite sides of OA. Then ∠OAB = ∠OAC .
Answer:
False
Justification:
Let AB and AC be the chord of the circle with center O on the opposite side of OA.
Consider the triangles AOC and AOB:
AO = AO (Common side in both triangles)
OB = OC (Both OB and OC are radius of circle)
But we can’t show that either the third side of both triangles are equal or any angle is equal.
Therefore ΔAOB is not congruent to ΔAOC.
∴ ∠OAB ≠ ∠OAC.
Video transcript
"hello student
welcome welcome back on a leader down
solving session again
and again today we come up with one one
new problem of mathematics right
basically this problem
is related to the geometry right okay
so quickly i will read the statement for
you two chords
a b and a c of the circles with center o
are on the opposite side of wave
then angle o a b is equals to angle of
oac so basically we need to check
whether this statement is correct or
wrong
right and to understand this what i have
done i have drawn this figure okay you
can see the figure here
all right okay now quickly we will
solve this problem right okay so from
this figure
okay we get two triangles here
right so one triangle is triangle
aoc and another triangle we get is
triangle a
ob all right okay so basically we are
getting the
two triangles here all right okay now
let's discuss
okay the sides of the triangle right so
in this particular triangle okay
side okay ao
is equals to side okay
ao right because both the triangles have
the common side
right so ao is a common side common side
right
okay that's why ao is equals to ao
right okay now what we will do we will
check
okay again we can see that okay length
of
oc length of oc
is equals to length of ob
right okay because ob and oc are the
radius of the circle right okay radius
of the
circle right so that's why okay
ob and oc are the equivalent
sides right okay they are having the
equivalent okay
but if you carefully observe that okay
ac for the side ac and
okay a b okay we can't say that whether
these sides are
equal or not right again we can't say
that
any of the angles are equal or not
that's why
we cannot predict the angle of a
o a b and o a c or equal or not right
and that's why angle at o
a b okay is
not equal to or it is not concurrent to
and
okay angle o a c okay
so basically these are not the
concurrent angle
so that's all all about today's session
please do comment if you have any doubt
and please subscribe to this channel
so that we will get the update for
upcoming video
bye
you"
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