Question 77
On the sides of triangle $ABC$ take the points $M_1$, $N_1$, $P_1$ such that each line $MM_1$, $NN_1$, $PP_1$ divides the perimeter of $ABC$ into two equal parts ($M$, $N$, $P$ are respectively the midpoints of sides $BC$, $CA$, $AB$).
1/ Prove that the lines $MM_1$, $NN_1$, $PP_1$ are concurrent at a point $K$.
2/ Prove that among the ratios $\frac{KA}{BC}$, $\frac{KB}{CA}$, $\frac{KC}{AB}$ there exists at least a ratio which is not less than $\frac{1}{\sqrt{3}}$.
1/ Prove that the lines $MM_1$, $NN_1$, $PP_1$ are concurrent at a point $K$.
2/ Prove that among the ratios $\frac{KA}{BC}$, $\frac{KB}{CA}$, $\frac{KC}{AB}$ there exists at least a ratio which is not less than $\frac{1}{\sqrt{3}}$.