Dubtem que el radi estigui recte.

Because dubtem que normally triggers the subjunctive in Catalan.

• dubtem = we doubt
• after verbs of doubt, uncertainty, emotion, desire, etc., Catalan often uses the subjunctive in the following clause
• the present subjunctive of estar for ell / ella / vostè is estigui

So:

• Dubtem que el radi està recte would sound wrong in standard Catalan
• Dubtem que el radi estigui recte is the expected structure

A very literal breakdown is:

• Dubtem = we doubt
• que = that
• el radi estigui recte = the radius/ray be straight

Even though English says is straight, Catalan uses the subjunctive here.

Estigui is the present subjunctive of estar.

Here is the present subjunctive of estar:

• jo estigui
• tu estiguis
• ell / ella / vostè estigui
• nosaltres estiguem
• vosaltres estigueu
• ells / elles / vostès estiguin

In the sentence, the subject of the subordinate clause is el radi, which is third-person singular, so Catalan uses estigui.

Here estar is used because recte describes a physical position or condition: something being straight, aligned, upright, or not bent.

So:

• estar recte = to be straight / upright
• ser would not be the natural choice here

This is similar to other Catalan uses of estar for conditions or positions.

For example:

• La barra està recta. = The bar is straight.
• Asseu-te recte. = Sit up straight.

So in Dubtem que el radi estigui recte, the idea is that the radius/ray may not be physically straight.

Here recte means straight.

It agrees with el radi, which is masculine singular, so the form is recte.

Agreement forms:

• masculine singular: recte
• feminine singular: recta
• masculine plural: rectes
• feminine plural: rectes

Examples:

• el radi recte
• la línia recta
• els cables rectes
• les barres rectes

Depending on context, recte can also mean things like upright or sometimes morally upright, but in this sentence the natural meaning is physical straightness.

Que introduces the subordinate clause, just like that in English.

• Dubtem que... = We doubt that...

So the sentence has two parts:

1. Dubtem = we doubt
2. que el radi estigui recte = that the radius/ray is straight

In everyday English, that is often omitted:

• We doubt the radius is straight

But in Catalan, que is normally kept in this structure.

Radi can mean different things depending on context. The most common possibilities are:

• radius in geometry
• ray or a radial line/beam in some technical contexts
• sometimes spoke in contexts like a wheel, depending on usage

Since you said the meaning is already shown to the learner, the key grammar point is that radi is:

• masculine
• singular

That is why the article is el and the adjective is in the masculine singular form:

• el radi
• recte

This is the normal Catalan order:

• main clause: Dubtem
• connector: que
• subject: el radi
• verb: estigui
• adjective/complement: recte

So it follows a very standard pattern: [main verb] + que + [subject] + [subjunctive verb] + [complement]

Catalan usually does not need to change the word order here for it to sound natural.

Usually no. In Catalan, the article is normally kept:

• el radi

English sometimes drops articles in technical notes or headings, but in a full sentence Catalan generally sounds more natural with the article.

So:

• Dubtem que radi estigui recte is not correct
• Dubtem que el radi estigui recte is correct

Yes. Dubtem is the 1st person plural present indicative of dubtar:

• jo dubto = I doubt
• tu dubtes = you doubt
• ell / ella dubta = he/she doubts
• nosaltres dubtem = we doubt
• vosaltres dubteu = you all doubt
• ells / elles dubten = they doubt

So Dubtem que... means We doubt that...

Yes, depending on nuance and context. For example:

• No estem segurs que el radi estigui recte. = We are not sure that the radius/ray is straight.
• Ens sembla dubtós que el radi estigui recte. = It seems doubtful to us that the radius/ray is straight.

But if you want the specific meaning of we doubt that..., then Dubtem que el radi estigui recte is a good direct structure.

The most important takeaway is this pattern:

dubtar que + subjunctive

So if you say that someone doubts something in Catalan, the following clause will usually use the subjunctive:

• Dubto que sigui veritat. = I doubt it is true.
• Dubtem que arribi a temps. = We doubt that he/she will arrive on time.
• Dubtem que el radi estigui recte. = We doubt that the radius/ray is straight.

If you remember that pattern, the sentence becomes much easier to understand and build.