Question : In the given figure, O is the centre of the circle, $\angle DAB=110^{\circ}$ and $\angle BEC=100^{\circ}$. What is the value (in degrees) of $\angle OCB$?
Option 1: 5
Option 2: 10
Option 3: 15
Option 4: 20
Correct Answer: 10
Solution : Given, $\angle DAB=110^{\circ}$ and $\angle BEC=100^{\circ}$ Since the angle subtended by the chord at the centre is double the angle subtended by the chord at the circumference, reflex$\angle BOC = 2\angle BEC = 200^\circ$ So, $\angle BOC = 360^\circ-200^\circ = 160^\circ$ By angle sum property in $\triangle BOC$, $\angle BOC + \angle OCB+ \angle OBC =180^\circ$ ⇒ $160^\circ+ 2\angle OCB =180^\circ$ ($\angle OCB = \angle OBC$ since OB and OC are radii of same circle) ⇒ $\angle OCB = 10^\circ$ Hence, the correct answer is 10.
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Question : Directions: Select the option figure that is NOT embedded in the figure (X) given below (rotation is NOT allowed).
Option 1:
Option 2:
Option 3:
Option 4:
Question : In the given figure, O is the centre of the circle, $\angle PQO=30^{\circ}$ and $\angle QRO=45^{\circ}$. What is the value (in degrees) of $\angle POR$?
Option 1: $150^{\circ}$
Option 2: $110^{\circ}$
Option 3: $160^{\circ}$
Option 4: $130^{\circ}$
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°
Question : Directions: Select the correct mirror image of the given figure when the mirror is placed at MN as shown.
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