AB is a chord of a circle with centre O, while PAQ is the tangent at A, R is a point on the minor arc AB. If ∠BAQ = 70°, then find the measure of ∠ARB.
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 110°
BAQ = 700
PAQ is tangent at A.
The angle subtended by an arc at the center is double than subtended by it on other parts of the circle.
PAQ is tangent at point A. Thus, ∠OAQ = 900
From figure -
∠OAB = ∠OAQ - ∠BAQ
∠OAB = 900 - 700 = 200
∠OBA = ∠OAB = 200 (Angle subtended by radius are equal)
In triangle OBA -
∠BOA = 1800 - (∠OBA + ∠OAB)
∠BOA = 1800 - (200 + 200) = 1800 - 400 = 1400
∠BOA (exterior angle) = 3600 - 1400 = 2200
∠ARB = (∠BOA)/2
∠ARB = (220)/2 = 1100