Question

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Answer 1

Answer:

∠AOB=∠COA

Draw OD⊥AB

In △AOB, OA=OB since both are radius of the circle.

∴∠OAD=∠OBD

Now, △AOB~△COB

⇒∠AOB=∠BOC=∠COA⇒∠AOB=∠BOC=∠COA=360°3=120°-------------------(1)

So, in △AOD, ∠AOD=∠AOB2

⇒∠AOD=120°2=60°

⇒∠OAD=30°

Now, cos ∠OAD=ADAO

⇒cos 30°=AD23√⇒3√2=AD23√⇒AD=3

⇒AB=2×3=6

And from (1),

AB=BC=CA

So, AB=BC=CA=6

Perimeter of △ABC=AB+BC+CA=6+6+6=18 units

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Answer 2

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