Question : In a circle, O is the centre of the circle. Chords AB and CD intersect at P. If $\angle AOD=32^{\circ}$ and $\angle CO B=26^{\circ}$, then the measure of $\angle APD$ lies between:

Option 1: 18º and 22º

Option 2: 26º and 30º

Option 3: 30º and 34º

Option 4: 22º and 26º

Question : In $\triangle {ABC}$, O is the incentre and $\angle {BOC}=135^{\circ}$. The measure of $\angle {BAC}$ is:

Option 1: 90º

Option 2: 55º

Option 3: 80º

Option 4: 45º

Question : In $\triangle A B C, \angle B=78^{\circ}, A D$ is a bisector of $\angle A$ meeting BC at D, and $A E \perp B C$ at $E$. If $\angle D A E=24^{\circ}$, then the measure of $\angle A C B$ is:

Option 1: 30$^\circ$

Option 2: 38$^\circ$

Option 3: 32$^\circ$

Option 4: 42$^\circ$

Question : In $\triangle {ABC}$, D is a point on BC such that $\angle {ADB}=2 \angle {DAC}, \angle {BAC}=70^{\circ}$ and $\angle {B}=56^{\circ}$. What is the measure of $\angle A D C$?

Option 1: $72^{\circ}$

Option 2: $54^{\circ}$

Option 3: $74^{\circ}$

Option 4: $81^{\circ}$

Question : $D$ is a point on the side $BC$ of a triangle $ABC$ such that $AD\perp BC$. $E$ is a point on $AD$ for which $AE:ED=5:1$. If $\angle BAD=30^{\circ}$ and $\tan \left ( \angle ACB \right )=6\tan \left ( \angle DBE \right )$, then $\angle ACB =$

Option 1: $30^{\circ}$

Option 2: $45^{\circ}$

Option 3: $60^{\circ}$

Option 4: $15^{\circ}$