ProofModerate1.5 marks
8(b)
In the given figure PQ is a tangent to the circle at A, AB and AD are bisectors of ∠CAQ and ∠PAC. If ∠BAQ = 30°, prove that:
BD is a diameter of the circle
Topic: Tangents / intersecting chords
Previous-year question practice database
Answer
Exam answer
∠BAQ = ∠BCA = 30o
Explanation
(i) AB is the bisector of ∠CAQ. ∴ ∠CAB = ∠BAQ = 30o AD is the bisector of ∠PAC ∴∠CAD = ∠PAD = 180° − 60° = = 60° ∴∠BAD = ∠BAC + ∠CAD = 30 + 60° = 90° ∴BD is a diameter of the circle. (ii) ∠BAQ = ∠BCA = 30o ∵ AB is a chord and PQ tangent ∴angle in the alternate segment are equal ∴ ∆ABC is an isosceles triangle. D C B A P Q