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 : ABCD is a cyclic quadrilateral such that AB is the diameter of the circle circumscribing it and $\angle $ADC = 118°. What is the measure of $\angle$BAC?

Option 1: 28°

Option 2: 45°

Option 3: 32°

Option 4: 30°

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 : Circum-centre of $\triangle PQR$ is O. If $\angle QPR=55^{\circ}$ and $\angle QRP=75^{\circ}$, What is the value (in degree) of $\angle OPR$?

Option 1: 45°

Option 2: 40°

Option 3: 65°

Option 4: 70°

Question : In a triangle, ABC, BC is produced to D so that CD = AC. If $\angle BAD=111^{\circ}$ and $\angle ACB=80^{\circ}$, then the measure of $\angle ABC$ is:

Option 1: 31°

Option 2: 33°

Option 3: 35°

Option 4: 29°