Question

PAQ is a tangent to circle with centre O, at a point A on it. AB is a chord such that ∠BAQ = x∘(x < 90). C is a point on the major

arc AB such that ∠ACB = y∘. If ∠ABO = 32∘, then the value of x + y is:​

Answer 1

Answer:

∠BAP=75

∘

∠OAP=90

∘

∴∠OAB=90

∘

−75

∘

=15

∘

So, ∠AOB=180

∘

−2(15

∘

)=150

∘

∴Exterior∠AOB=360

∘

−150

∘

=210

∘

So, ∠ACB=

2

1

(210

∘

)=105

∘

[Angle subtended by an arc at the centre is double than the angle subtended by it at the remaining part of the circle]