Question : Two chords AB and CD of a circle with centre O intersect at P. If $\angle$ APC = 40º, then the value of $\angle$AOC + $\angle$BOD is:

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:

Question : ABC is an isosceles triangle having AB = AC and $\angle$A = 40$^\circ$. Bisector PO and OQ of the exterior angle $\angle$ ABD and $\angle$ ACE formed by producing BC on both sides, meet at O, then the value of

Question : If O is the orthocenter of a triangle ABC and $\angle$ BOC = 100$^\circ$, then the measure of $\angle$BAC is ____.

Question : Two chords of a circle, $\overline{\mathrm{AB}}$ and $\overline{\mathrm{CD}}$, meet outside the circle at the point $\mathrm{P}$. If $\mathrm{m}(\overline{\mathrm{AP}})=200 \mathrm{~mm}, \mathrm{~m}(\overline{\mathrm{AB}})$ $=120 \mathrm{~mm}$, and