PAQ is a tangent to a circle with center O, at a point A unit. AB is a chord such that ∠BAP = x° (x < 90°). C is a point on the major arc AB such that ∠ACB = y°. If ∠ABO = 35°, then the value of x + y is :
Answer & explanation
Correct answer: option 2
AO = BO
⇒ ABO = ∠BAO = 35°
and ∠OAQ = 90° (angle by radius on tangent)
⇒ x° + 35° = 90°
x° = 55°
and we know, x° = y°
⇒ x + y = 55 + 55 = 110°