Question : If the angle between two radii of a circle is $100^{\circ}$, then the angle between the tangents at the ends of the radii will be:

Option 1: $90^{\circ}$

Option 2: $70^{\circ}$

Option 3: $80^{\circ}$

Option 4: $50^{\circ}$

Question : If the angle made by a chord on the major arc of a circle is $50^{\circ}$, then what will be the angle made by the same chord on the minor arc of this circle?

Option 1: $120^{\circ}$

Option 2: $130^{\circ}$

Option 3: $80^{\circ}$

Option 4: $100^{\circ}$

Question : $O$ is the orthocentre of triangle $ABC$, and if $\angle BOC = 110^\circ$, then $\angle BAC$ will be:

Option 1: $110^\circ$

Option 2: $70^\circ$

Option 3: $100^\circ$

Option 4: $90^\circ$

Question : In $\Delta ABC$, the external bisector of the angles, $\angle B$ and $\angle C$ meet at the point $O$. If $\angle A = 70^\circ$, then the measure of $\angle BOC$:

Option 1: $55^\circ$

Option 2: $75^\circ$

Option 3: $60^\circ$

Option 4: $50^\circ$

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 : ABCD is a cyclic quadrilateral, AB is the diameter of the circle. If angle $\angle ACD=45^{\circ}$, then what is the value of $\angle BAD$?

Option 1: $90^{\circ}$

Option 2: $45^{\circ}$

Option 3: $135^{\circ}$

Option 4: $35^{\circ}$