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A, B and C are three points on a circle with centre O. The tangent at C meets BA produced to T. If ∠ATC = 30° and∠ACT = 48°, then what is the value of ∠AOB ?
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- 78°
- 96°
- 102°
- 108°
- 78°
Correct Option: D
According to question , we draw a figure circle with centre O in which A, B and C are three points 
Here , ∠ATC = 30°;
∠ACT = 48°
From ∆ CAT ,
∴ ∠CAT + ∠ACT + ∠ATC = 180°
∴ ∠CAT = 180° – (30° + 48°) = 180° – 78° = 102°
∴ ∠OCA = 90° – 48° = 42° = ∠OAC
∴ ∠OAB = 180° – 102° – 42° = 36° = ∠OBA
∴ ∠AOB = 180° – 2 × 36° = 108°
