I proposed my conjecture generalization of Erdős–Mordell inequality as following:
Let $A_1A_2....A_n$ be a polygon in a plane, $P$ be the point on the planein $A_1A_2....A_n$. Let $d_i$ be the distances from $P$ to $A_iA_{i+1}$, for $i=1,...,n$ and $A_{i+1}=A_1$. Then:
$$\sum_{1}^{n}{ PA_i} \ge \frac{1}{cos{\frac{\pi}{n}}}\sum_{1}^{n}{d_i} $$
Equality holds when $A_1A_2....A_n$ be the regular polygon, and $P$ is its center.
I proposed my conjecture generalization of Erdős–Mordell inequality as following:
Let $A_1A_2....A_n$ be a polygon in a plane, $P$ be the point on the plane. Let $d_i$ be the distances from $P$ to $A_iA_{i+1}$, for $i=1,...,n$ and $A_{i+1}=A_1$. Then:
$$\sum_{1}^{n}{ PA_i} \ge \frac{1}{cos{\frac{\pi}{n}}}\sum_{1}^{n}{d_i} $$
Equality holds when $A_1A_2....A_n$ be the regular polygon, and $P$ is its center.
I proposed my conjecture generalization of Erdős–Mordell inequality as following:
Let $A_1A_2....A_n$ be a polygon in a plane, $P$ be the point in $A_1A_2....A_n$. Let $d_i$ be the distances from $P$ to $A_iA_{i+1}$, for $i=1,...,n$ and $A_{i+1}=A_1$. Then:
$$\sum_{1}^{n}{ PA_i} \ge \frac{1}{cos{\frac{\pi}{n}}}\sum_{1}^{n}{d_i} $$
Equality holds when $A_1A_2....A_n$ be the regular polygon, and $P$ is its center.
I proposed my conjecture generalization of Erdős–Mordell inequality as following:
Let $A_1A_2....A_n$ be a polygon in a plane, $P$ be the point on the plane. Let $d_i$ be the distances from $P$ to $A_iA_{i+1}$, for $i=1,...,n$ and $A_{i+1}=A_1$. Then:
$$\sum_{1}^{n}{ PA_i} \ge \frac{1}{cos{\frac{\pi}{n}}}\sum_{1}^{n}{d_i} $$
Equality holds when $A_1A_2....A_n$ be the regular polygon, and $P$ is its center.
I proposed my conjecture generalization of Erdős–Mordell inequality as following:
Let $A_1A_2....A_n$ be a polygon in a plane, $P$ be the point on the plane. Let $d_i$ be the distances from $P$ to $A_iA_{i+1}$. Then:
$$\sum_{1}^{n}{ PA_i} \ge \frac{1}{cos{\frac{\pi}{n}}}\sum_{1}^{n}{d_i} $$
Equality holds when $A_1A_2....A_n$ be the regular polygon, and $P$ is its center.
I proposed my conjecture generalization of Erdős–Mordell inequality as following:
Let $A_1A_2....A_n$ be a polygon in a plane, $P$ be the point on the plane. Let $d_i$ be the distances from $P$ to $A_iA_{i+1}$, for $i=1,...,n$ and $A_{i+1}=A_1$. Then:
$$\sum_{1}^{n}{ PA_i} \ge \frac{1}{cos{\frac{\pi}{n}}}\sum_{1}^{n}{d_i} $$
Equality holds when $A_1A_2....A_n$ be the regular polygon, and $P$ is its center.
I proposed my conjecture generalization of Erdős–Mordell inequality as following:
Let $A_1A_2....A_n$ be a polygon in a plane, $P$ be the point on the plane. Let $d_i$ be the distancedistances from $P$ to $A_iA_{i+1}$. Then:
$$\sum_{1}^{n}{ PA_i} \ge \frac{1}{cos{\frac{\pi}{n}}}\sum_{1}^{n}{d_i} $$
Equality holds when $A_1A_2....A_n$ be the regular polygon, and $P$ is its center.
I proposed my conjecture generalization of Erdős–Mordell inequality as following:
Let $A_1A_2....A_n$ be a polygon in a plane, $P$ be the point on the plane. Let $d_i$ be the distance from $P$ to $A_iA_{i+1}$. Then:
$$\sum_{1}^{n}{ PA_i} \ge \frac{1}{cos{\frac{\pi}{n}}}\sum_{1}^{n}{d_i} $$
Equality holds when $A_1A_2....A_n$ be the regular polygon, and $P$ is its center.
I proposed my conjecture generalization of Erdős–Mordell inequality as following:
Let $A_1A_2....A_n$ be a polygon in a plane, $P$ be the point on the plane. Let $d_i$ be the distances from $P$ to $A_iA_{i+1}$. Then:
$$\sum_{1}^{n}{ PA_i} \ge \frac{1}{cos{\frac{\pi}{n}}}\sum_{1}^{n}{d_i} $$
Equality holds when $A_1A_2....A_n$ be the regular polygon, and $P$ is its center.