Question

Is AO = OB ?! How?...........​

Answer 1

in triangle AOT. and BOT

At = Bt =12 cm

OT is common

so both triangle are congrant so we can say that AO will be equal to OB

Answer 2

If you can show ∆TBO and ∆TAO are congruent, then BO = AO.

To show congruency,

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in ∆TBO and ∆TAO:

TB = TA (given)

Angle BTO = Angle ATO (how? you have to show it)

TO = TO (given)

Thus ∆TBO and ∆TAO congruent by SAS rule.

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Thus OA = OB

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Coming to Angle BTO = Angle ATO (how? you have to show it)

Since BA is tangent to circle, AOT = BOT = 90

Since ∆TAB is isosceles, TBO = TAO

Two of the angles of the triangles are same.

So third will also be same.(How?)

Hence BTO = ATO