YesIf the arcs bend the other way, then "yes"; otherwise there is an obvious counterexample.
Note that the statement holds if $c\in [a,b]$. Moreover, if the arcs $ac$ and $bc$ are tangent to the arc $ab$ at $a$ and $b$ respectively, then equality holds. Furthermore, note that we can assume that $ac$ and $bc$ are tangent to $ab$.
On the following diagram, if arcs look tangent, then they are.
Observe that $|ab|=|ac|+|cx|+|xb|\geqslant |ac|+|cb|$, where $|{*}{*}|$ denotes the length of the arc.
Yes.
Note that the statement holds if $c\in [a,b]$. Moreover, if the arcs $ac$ and $bc$ are tangent to the arc $ab$ at $a$ and $b$ respectively, then equality holds. Furthermore, note that we can assume that $ac$ and $bc$ are tangent to $ab$.
On the following diagram, if arcs look tangent, then they are.
Observe that $|ab|=|ac|+|cx|+|xb|\geqslant |ac|+|cb|$, where $|{*}{*}|$ denotes the length of the arc.
If the arcs bend the other way, then "yes"; otherwise there is an obvious counterexample.
Note that the statement holds if $c\in [a,b]$. Moreover, if the arcs $ac$ and $bc$ are tangent to the arc $ab$ at $a$ and $b$ respectively, then equality holds. Furthermore, note that we can assume that $ac$ and $bc$ are tangent to $ab$.
On the following diagram, if arcs look tangent, then they are.
Observe that $|ab|=|ac|+|cx|+|xb|\geqslant |ac|+|cb|$, where $|{*}{*}|$ denotes the length of the arc.
Yes.
Note that equalitythe statement holds if $c\in [a,b]$.
Furthermore Moreover, note that we can assume thatif the arcs $ac$ and $bc$ are tangent to thethe arc $ab$ at $a$ and $b$ respectively, then equality holds. Furthermore, note that we can assume that $ac$ and $bc$ are tangent to $ab$.
On the following diagram, if arcs look tangent, then they are assumed to be tangent.
Observe that $|ab|=|ac|+|cx|+|xb|\geqslant |ac|+|cb|$, where $|{*}{*}|$ denotes the length of the arc.
Yes.
Note that equality holds if $c\in [a,b]$.
Furthermore, note that we can assume that arcs $ac$ and $bc$ are tangent to the arc $ab$ at $a$ and $b$ respectively.
On the following diagram, if arcs look tangent, then they are assumed to be tangent.
Observe that $|ab|=|ac|+|cx|+|xb|\geqslant |ac|+|cb|$, where $|{*}{*}|$ denotes the length of the arc.
Yes.
Note that the statement holds if $c\in [a,b]$. Moreover, if the arcs $ac$ and $bc$ are tangent to the arc $ab$ at $a$ and $b$ respectively, then equality holds. Furthermore, note that we can assume that $ac$ and $bc$ are tangent to $ab$.
On the following diagram, if arcs look tangent, then they are.
Observe that $|ab|=|ac|+|cx|+|xb|\geqslant |ac|+|cb|$, where $|{*}{*}|$ denotes the length of the arc.
Yes.
Note that equality holds if $c\in [a,b]$.
Furthermore, note that we can assume that arcs $ac$ and $bc$ are tangent to the arc $ab$ at $a$ and $b$ respectively.
On the following diagram, if arcs look tangent, then they are assumed to be tangent.
Observe that $|ab|=|ac|+|cx|+|xb|\geqslant |ac|+|cb|$, where $|{*}{*}|$ denotes the length of the arc.
