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.

Answer 1

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°