NCERT Exemplar Solutions Class 9 Mathematics Solutions for Circles - Exercise 10.2 in Chapter 10 - Circles

Question 3 Circles - Exercise 10.2

Two chords AB and AC of a circle with centre O are on the opposite sides of OA. Then ∠OAB = ∠OAC .




Let AB and AC be the chord of the circle with center O on the opposite side of OA.

NCERT Exemplar Solutions - Mathematics - class 9 chapter Circles Question 3 Solution image

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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