Question : ABCD is a cyclic quadrilateral such that AB is the diameter of the circle circumscribing it and $\angle A D C=148^{\circ}$. What is the measure of the $\angle BAC$?

Option 1: $32^{\circ}$

Option 2: $45^{\circ}$

Option 3: $58^{\circ}$

Option 4: $60^{\circ}$

Question : ABCD is a cyclic quadrilateral. The tangents to the circle at the points A and C on it, intersect at P. If $\angle\mathrm{ABC}=98^{\circ}$, then what is the measure of $\angle \mathrm{APC}$ ?

Option 1: 22°

Option 2: 26°

Option 3: 16°

Option 4: 14°

Question : AB is a chord in a circle with centre O. AB is produced to C such that BC is equal to the radius of the circle. C is joined to O and produced to meet the circle at D. If $\angle \mathrm{ACD}=32^{\circ}$, then the measure of $\angle \mathrm{AOD}$ is _____.

Option 1: 48°

Option 2: 96°

Option 3: 108°

Option 4: 80°

Question : PQRS is a cyclic quadrilateral. If $\angle P$ is 4 times $\angle R$, and $\angle S$ is 3 times $\angle Q$, then the average of $\angle Q$ and $\angle R$ is:

Option 1: 40.5°

Option 2: 45.7°

Option 3: 90°

Option 4: 81°

Question : In the following figure, AB is the diameter of a circle whose centre is O. If $\angle AOE=150^{\circ},\angle DAO=51^{\circ}$ then the measure of $\angle CBE$ is:

Option 1: 115°

Option 2: 110°

Option 3: 105°

Option 4: 120°