Hey guys

The sides of triangle ABC are divided into segments of lengths a, b and x by the inscribed circle of centre O and radius r as shown. Find x in terms of a, b and r.

The first part of the answer by the teacher is as shown:

Let $\displaystyle \angle OAB = \alpha$ and $\displaystyle \angle OBA = \beta$

Therefore, $\displaystyle \angle OCA = 90 – (\alpha + \beta)$

So $\displaystyle tan (90 – (\alpha + \beta)) = \frac{x}{r}$

….

Could someone please explain to me how $\displaystyle tan (90 – (\alpha + \beta)) = \frac{x}{r}$? For some reason, all I seem to be able to get is $\displaystyle tan (90 – (\alpha + \beta)) = \frac{x}{r}$.

Thanx.