Question : $\mathrm{O}$ is the centre of a circle and $\mathrm{A}$ is a point on a major arc $\mathrm{BC}$ of the circle. $\angle \mathrm{BOC}$ and $\angle \mathrm{BAC}$ are the angles made by the minor arc $\mathrm{BC}$ on the centre and circumference, respectively. If $\angle \mathrm{ABO}=40^{\circ}$ and $\angle \mathrm{ACO}=30^{\circ}$, then find $\angle \mathrm{BOC}$.

Option 1: $130^{\circ}$

Option 2: $140^{\circ}$

Option 3: $120^{\circ}$

Option 4: $150^{\circ}$

Question : The angle subtended by a chord on the major arc of the circle is 50°. What is the angle subtended by the same chord on the centre of the circle?

Option 1: 100°

Option 2: 120°

Option 3: 140°

Option 4: 25°

Question : The chord of a circle is equal to its radius. The angle (in degrees) subtended by this chord at any point on the minor arc of the circle is:

Option 1: 130°

Option 2: 140°

Option 3: 150°

Option 4: 120°

Question : If $ABCD$ is a cyclic quadrilateral with $\angle A=50^{\circ},\angle B=80^{\circ}$, then $\angle C$ and $ \angle D$ are:

Option 1: $100^{\circ}$ and $130^{\circ}$

Option 2: $115^{\circ}$ and $115^{\circ}$

Option 3: $110^{\circ}$ and $120^{\circ}$

Option 4: $130^{\circ}$ and $100^{\circ}$

Question : The sum of the angles made by a chord at the centre and on the major arc of a circle is 225°. What will be the angle made at the major arc of this circle?

Option 1: 125 degrees

Option 2: 150 degrees

Option 3: 90 degrees

Option 4: 75 degrees