PAQ is a tangent to the circle with center O at a point A as shown in figure. If ∠OBA=35∘, find the value of ∠BAQ and ∠ACB. [4 MARKS]
Concept: 1 Mark
Application: 3 Marks
OB = OA (radius)
⇒∠OBA=∠OAB=35∘
From △OAB,∠OBA+∠OAB+∠AOB=180∘
35∘+35∘+∠AOB=180∘
∠AOB=110∘
But ∠ACB=12 ∠AOB
⇒∠ACB=12 (110∘)
∠ACB=55∘
As the tangent at any point of a circle is perpendicular to the radius through the point of contact,
∠OAQ=90∘
∠BAQ=∠OAQ−∠OAB
∠BAQ=90∘−35∘
∠BAQ=55∘
Therefore ∠ACB=55∘ and ∠BAQ=55∘