Question 35
From point $P$ outside a circle, with a circumference of $10$ units, a tangent is drawn. Also from $P$ a secant is drawn dividing the circle into unequal arcs with lengths $m$ and $n.$ It is found that $t,$ the length of the tangent, is the mean proportional between $m$ and $n.$ If $m$ and $t$ are integers, then $t$ may have the following number of values: