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Slopes of an Isosceles Triangle

Geometry · 26th PMO Qualifying Stage 1500
Three lines with slope 1, 7, and $c$ intersect to form a nondegenerate isosceles triangle. If $1<c<7$, what is $c$?
A$\dfrac{8}{7}$ B$\dfrac{13}{7}$ C$2$ D$\dfrac{15}{7}$