GoodnessShallPrevail wrote:

∠ABC = 90°

Per Right Triangle Altitude Theorem:

AB square = AO X AC

AO = OC = 8

AC = AO + OC = 16

AB square = 8 X 16 = 128

Hence, AB could be determined from the Q stem itself.

So, irrespective of what information is given in each Statement, AB will be determined.

Hence, answer is D even before reviewing Statement 1 and Statement 2.

Please suggest whether the aforementioned is correct or not.

My friend sorry to break it to you but above highlighted are a couple of incorrect statement in your method.

I am not sure from where did you get this Right Triangle Altitude Theorem because, in actual Altitude Theorem, the line segment BO has to have an angle of 90 Degree with line segment AC. (that is how you can call BO an altitude of the triangle.)

Hence, you are getting a wrong calculation.

Here is how I would approach this :

We are asked to find AB.

Now, Triangle ABC is a right angle triangle.

So, AC^2 = AB^2 + BC^2

i.e AB^2 = AC^2 - BC^2

Now we know AC = 8 (twice the radius OC or OA or BO)

And if we know BC, we can find AB.

Hence, effectively, this question is to find BC.

Moving to the statements,

St-1 : Angle AOB = 120.

So, In triangle AOB, Since AO=OB (both are radius), Angle OAB = Angle OBA

So from, Angle OAB + Angle OBA + Angle AOB = 180

2*(Angle OBA) = 180-120 = 60

So angle OBA = 30

Therefore, Angle OBC = 90-30 = 60.

Hence, in the triangle, OBC, all angles are 60.

Therefore, its an equilateral triangle and all sides have length 8 (same as radius OC).

So, BC = 8.

Hence this statement is sufficient.

Statement-2 :

OB = BC

Pretty straight forward, OB = radius = 8 = BC

Hence, we got BC and so can calculate AB.

So, this statement is sufficient as well.

OPtion D is the correct answer.

P.S : If you were to calculate the value of AB, it would be 8Sqrt3. (which is NOT same as what you were calculating).

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