Here is the question - Two chords AB and CD of a circle with centre O , Intersect each other at P. If angle AOD = 100 and angle BOC= 70. Find value of angle APC.
Now I know how to solve this kind of problems ( See the image ) but only when I follow a specific approach , that is to take the 4 points across the circle. If I try to solve this problem by taking points on the same side of circle. I can't solve it. Can anyone please tell me how to solve it by that method. ( See attach image for better understanding)
I like the following way.
Since $\widehat{AD}=100^{\circ},$ we obtain: $$\widehat {DB}=180^{\circ}-100^{\circ}=80^{\circ}.$$ Also, $$\widehat{AC}=180^{\circ}-70^{\circ}=110^{\circ}.$$ Ids est, $$\measuredangle APC=\frac{1}{2}(80^{\circ}+110^{\circ})=95^{\circ}.$$