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.
58∘
In ΔOBC,OB=OC (radii of same circle)
∴∠OBC=∠OCB =2∠OBC
⇒64∘=2∠OBC
∴∠OBC=64∘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∘=58∘