The problem: Let A be an outside point from the circle with the center O. Draw the secant ABC of the mentioned circle. The tangents at B and C got an intersection, named K. From K, we draw the perpendicular to AO. Name the intersection H. E and F are 2 intersections of KH and the circle with the center O. (E is between K and F). We name M for the intersection of KO and BC. Prove that:
- There exists a circle that pass throught 4 points E, M, O and F
- AE and AF are tangents of the circle with center O
- I tried to translate this problem from my language to English. So If I use wrong grammar structure or wrong expression, please forgive me.
- This is not my homework. I like to look for and solve "hard" problems, by my view. This is one of those, and I can't find out the way to solve it.