In a convex quadrilateral $\displaystyle ABCD$, $\displaystyle AB=BC+DA.$ Bisectors of ABC and BAD meet at $\displaystyle P$. Show that $\displaystyle CP=DP$.
Sadly, no ideas on this one.
In a convex quadrilateral $\displaystyle ABCD$, $\displaystyle AB=BC+DA.$ Bisectors of ABC and BAD meet at $\displaystyle P$. Show that $\displaystyle CP=DP$.
Sadly, no ideas on this one.
1. I assume that you mean the angle bisector ... ? (Drawn in blue) If so:
2. Draw a sketch (see attachment)
3. For symmetry reasons the 2 orange segments must be as long as the red segment.