How to mark the inverse of a line length using Geometry?

Question

Using some Geometry construction, how can we show the length 1/c on this figure (so that we end up depicting the inverse length)? Bottom line, You can make any construction, but given length c of this right angle triangle, show/create/mark something which equals 1/c.

Assume length b = 1 unit.

You don't have a length $1$ in your drawing. Without that, $\frac1c$ is meaningless. — Arthur, Sep 20 '19 at 05:17
You can assume side b to be a unit length -- i have edited the question. Thanks — Lemur, Sep 20 '19 at 05:23

score 1 · Accepted Answer · answered Sep 20 '19 at 05:28

Draw a circle of radius $b$ centered at the intersection of $b$ and $c$. This circle intersects $c$. From that intersection, draw a line parallel to $a$ down to $b$. This new triangle (part of $b$, part of $c$, and the new line) is similar to the large triangle, with hypotenuse length equal to $b$. So the leg along $b$ has length $\frac bc$.

How to mark the inverse of a line length using Geometry?

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