I am studying for a bachelor's degree in math at a Brazilian university. I am in the first semester studying euclidian geometry. In the second chapter of the book there is this problem:
how to prove that a segment line between a point inside a circle and a point outside a circle has a point in common with the circle? Until now we only saw few axioms and theorems. In chapter two there are these sentences:
-There is a two-way correspondence, a bijective function, between each point in a line and a real number. The difference between any two numbers is the distance between the corresponding points.
-if the point C is between A and B,then, $\overline{AC}+\overline{BC}=\overline{AB}$
-If in a semi-line $S_{AB}$ there are a segment line $AC$ with $\overline{AC}<\overline{BC}$, then the point C is between A and B
--Be the points A, B, C different points in the same line whose coordinates are a, b, c. The point C is between A and B if , and only if, a
-Every line segment has an only one midpoint. the midpoint of a segment AB is a point C that $\overline{AC}=\overline{CB}$
-there are too the definition of circle, point inside a circle and point outside a circle
-Be A,B,C points in a plan,then, $\overline{AC}\leqslant\overline{AB}+\overline{BC}$
How can i solve the problem using this sentences?