CDS Model Paper 5 Mathematics

Given AB is a circle and BT is a tangent, ∠BAO=32°
Here, ∠OBT=90°
[ ∵ Tangent is ⊥ to the radius at the point of contact] OA=OB [ Radii of the same circle]
∴ ∠OBA=∠OAB=32° [ Angles opposite to equal side are equal]
∴ ∠OBT=∠OBA+∠ABT=90° or 32°+x=90°
∠x=90°−32°=58°
Also, ∠AOB=180°−∠OAB−∠OBA
=180°−32°−32°=116°
Now Y=

1

2

AOB [ Angle formed at the center of a circle is double the angle formed in the remaining part of the circle]
=

1

2

×116°=58°