Question

In the following figure, O is the center of circle. PAQ is the tangent of circle at point A. If ∠OBA = 32°, then find the value of x and y.

Answer 1

In ∆OAB

∵ OA = OB (radii of a circle)

∴ ∠OBA = ∠OAB (Opposite angle of the equal side of triangle)

∴ ∠OAB = 32°

⇒ ∠x = 32°

(∠OBA = 32°) …..(i)

Again, PAQ the tangent at point A of circle and OA is radius.

∴ OA ⊥ PQ

⇒ ∠OAQ = 90°

∴ ∠BAQ + ∠OAB = 90°

∴ ∠BAQ + 32° = 90° [∵ ∠OAB = 32°]

∠BAQ = 90° – 32° = 58°

∠BAQ = ∠ACB [angle made in alternate segment]

58° = ∠y

∠x = 32°, ∠y = 58°