You should not do it in paint, you should learn to build your own tools, and this can be done in Wolfram Mathematica.
You can add an Epilog
to your Plot
with a Triangle
and a Disk
at the correct coordinates.
Epilog -> {Red,
Triangle[Map[Plus[{4.8, 1.45}, #] &, {{0, 0}, {0.33, 1}, {-0.33, 1}}]],
Pink, Disk[{4.8, 1.45} + {0, 1}, {0.33, 0.1}]}
From your Plot
With[{p = {-8, -5, 0},sol = {4.8, 1.45}},
Plot[{(r + 3 Log[Abs[r - 3]] + p), -(r + 3 Log[Abs[r - 3]] + p)}, {r,
0, 10}, PlotRange -> {0, 10},
Ticks -> {{{3, Subscript["r", s]}}, {0}}, AxesLabel -> {r, ct},
AxesStyle -> Arrowheads[Small], ImageSize -> Large,
Epilog -> {Red,
Triangle[Map[Plus[sol, #] &, {{0, 0}, {0.33, 1}, {-0.33, 1}}]],
Pink, Disk[sol + {0, 1}, {0.33, 0.1}]}]
]

Obviously you will need to find and define the points and triangle sizes. That also can be done programmatically in Mathematica by finding the intersections and the slopes at the intersections.
Finding Solutions
sols = N@DeleteDuplicates[
Flatten[
Quiet@Select[
Map[
ReplaceAll[{r, #[[1]], 1/D[#[[1]], r], 1/D[#[[2]], r]},
NSolve[Equal @@ #, r, Reals]] &,
Permutations[
Flatten[{(r + 3 Log[Abs[r - 3]] +
p), -(r + 3 Log[Abs[r - 3]] + p)} /.
p -> {-8, -5, 0}], {2}]]
, NumberQ[#[[1, 2]]] &
], 1]] /. {Abs'[x_?Negative] -> -1, Abs'[x_?Positive] -> 1}
With[{p = {-8, -5, 0}},
Plot[{(r + 3 Log[Abs[r - 3]] + p), -(r + 3 Log[Abs[r - 3]] + p)}, {r,
0, 10}, PlotRange -> {0, 10},
Ticks -> {{{3, Subscript["r", s]}}, {0}}, AxesLabel -> {r, ct},
AxesStyle -> Arrowheads[Small], ImageSize -> Large,
Epilog -> {
Darker[Yellow]
, Table[
Triangle[
Map[Plus[sol[[1 ;; 2]], #] &, {{0, 0}, {sol[[3]], 1}, {sol[[4]],
1}}]], {sol, sols}]
, Yellow, EdgeForm[Thin]
, Table[
Disk[sol[[1 ;; 2]] + {0, 1}, {Abs[Subtract @@ (sol[[{4, 3}]])]/2,
0.1}], {sol, sols}]
}]
]
