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Question
In the given figure, AB is the diameter of the circle, with centre O, and AT is the tangent. Calculate the numerical value of x.
Solution
In ΔOBC,
OB = OC ...(Radii of the same circle)
∴ ∠OBC = ∠OCB
But, Ext. ∠COA = ∠OBC + ∠OCB
Ext. ∠COA = 2∠OBC
`=>` 64° = 2∠OBC
∴ ∠OBC = `64^circ/2` = 32°
Now in ΔABT,
∠BAT = 90° ...(OA ⊥ AT)
∠OBC or ∠ABT = 32°
∴ ∠BAT + ∠ABT + x° = 180°
`=>` 90° + 32° + x° = 180°
`=>` 122° + x° = 180°
`=>` x° = 180° – 122°
`=>` x° = 58°
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