Here are geometry problems which are inter-related:- Q1.In a triangle ABC, point P is taken so that angle ABP=30 degree, angle PBC=70 degree and angle PCB=10 degree=angle PCA.Find angle BAP. Q2.-In a triangle ABC, point P is taken so that angle ABP=70 degree, angle PBC=10 degree=angle PCB and angle PCA=30 degree.Find angle BAP.
In one of my previous mail I had mentioned that Dave Rusin had given a list of combination of angles where point is taken inside the triangle and 6 formed angles are multiples of 10 degree.Combination related to problem Q2 is [70,10,10,30,20,40] and this combination was absent in Dave Rusin's list. Rusin's list contained 74 total combinations.There are total 43 interesting combinations which are non-trivial and non obvious.I have solved 42 of them, one case is still unsolved.We can form a problem if we give 4 angles out of 6.So with one combination we can form C(6,4)=15 problems.So we have total of 43*15=645 , real bad problems.I think I am not wrong if I say that if we solve one of 15 then all 15 are solved.But if we try to find direct solution of all 15 then all have different type of solution.If some person has got lot of free time then he can try to find direct solution of all 15.Even among 43 problems we can find inter-relation with some simple construction as in above 2 problems. I will write more in coming mails.
**No response is depressing.I hope I am doing something which has got some worth.**