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Answer:

∠AOB = 36°

Angle subtended by chord AB at centre = 144°

Step-by-step EXPLANATION:

To find-----> AC = AB , ∠ ABC = 72° , OA and OB are tangents .

To find------>

1) ∠ AOB

2) Angle subtended by the chord AB at the centre .

Solution------> In Δ ABC ,

AC = AB ( given )

=> ∠ ABC = ∠ ACB = 72° ( angles opposite to EQUAL sides are equal )

Let centre of circle is O¹ , so angle subtended by chord on centre is ∠BO¹A .

Now , we know that angle subtended by a chord at centre is twice the angle subtended at circumference , so ,

∠ BO¹A = 2 ∠ ACB

= 2 ( 72° )

= 144°

Now , we know that,

∠ O¹AO = ∠O¹BO = 90° ( angle between tangent and radius is right angle )

Now , O¹ AOB is a quadrilateral so,

∠BO¹A + ∠O¹AO + ∠AOB + ∠OBO¹ = 360°

=> 144° + 90° + ∠AOB + 90° = 360°

=> ∠AOB = 360° - 324°

=> ∠AOB = 36°


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