Mathematics
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 diameter of the circle.

Related Questions
PT is a tangent to the circle at T. If ∠ABC = 70° and ∠ACB = 50°; calculate :
(i) ∠CBT
(ii) ∠BAT
(iii) ∠APT
In the given figure, O is the center of the circumcircle ABC. Tangents A and C intersect at P. Given angle AOB = 140° and angle APC = 80°; find the angle BAC.
Chords AB and CD of a circle intersect each other at point O such that OA : OC = 4 : 7. Then OB : OD is equal to :
4 : 7
5 : 4
7 : 4
4 : 5
If ∠PAC : ∠PCA = 4 : 5, ∠P is :
40°
60°
105°
45°