Akár rövid, akár hosszú a kör, nem hagyjuk ki.

Here akár ... akár ... means whether ... or ....

So:

• Akár rövid, akár hosszú a kör = Whether the round/lap is short or long

This pattern is very common in Hungarian when presenting two alternatives that do not change the main result.

A few similar patterns:

• Akár esik, akár fúj, elmegyünk.
  = Whether it rains or the wind blows, we’re going.
• Akár igaz, akár nem, érdekes.
  = Whether it’s true or not, it’s interesting.

Note that akár can mean other things in other contexts too, but in this structure it is best understood as whether.

Because Hungarian often avoids repeating a verb when it is understood from the second part.

The full underlying idea is:

• Akár rövid a kör, akár hosszú a kör...

But Hungarian prefers the shorter, smoother version:

• Akár rövid, akár hosszú a kör...

Also, in the present tense, 3rd person singular, the verb van (is) is usually omitted:

• A kör rövid. = The round is short.
• A kör hosszú. = The round is long.

So in this sentence, the meaning is still clear even though the verb is not repeated.

Both are possible, but the word order changes the emphasis.

• A kör hosszú = The round is long.
  This is more neutral.
• Hosszú a kör = The round is long.
  This puts more focus on hosszú.

In Akár rövid, akár hosszú a kör, the contrast is between rövid and hosszú, so Hungarian naturally puts those adjectives in the emphasized position.

That is why the sentence is not centered on the round, but on the two contrasting qualities:

• short
• long

A is the definite article, meaning the.

So:

• a kör = the round / the lap / the route

Hungarian often uses the definite article where English might also use the, but sometimes it appears in places that feel a little more natural or automatic in Hungarian than in English.

In this sentence, a kör refers to a specific round/lap/route understood from context, not just the general concept of roundness.

Literally, kör can mean several things depending on context, for example:

• circle
• round
• lap
• route
• turn

In this sentence, kör most likely means something like:

• round
• lap
• loop
• route

The exact English word depends on the situation. For example:

• in sports: lap
• in a game: round
• in running/walking/cycling: route or loop

So the grammar of the sentence stays the same, but the best translation of kör depends on context.

It means we do not skip it or we are not leaving it out.

This comes from the verb:

• kihagyni = to leave out, omit, skip

In the sentence, it appears as:

• nem hagyjuk ki

That is because Hungarian verbal prefixes often move away from the verb in negative sentences.

Compare:

• Kihagyjuk. = We skip it.
• Nem hagyjuk ki. = We do not skip it.

So:

• ki is the verbal prefix
• hagyjuk is the conjugated verb
• nem negates it

Because Hungarian has two types of verb conjugation:

• indefinite
• definite

Here the verb is in the definite conjugation:

• hagyjuk

That is used when the direct object is definite, specific, or already known.

In this sentence, the object is not said explicitly, but it is understood as something like:

• a kört = the round/lap
• or simply it

Since the object is definite and understood from context, Hungarian uses:

• nem hagyjuk ki

Compare:

• hagyunk valamit = we leave/skip something
• hagyjuk = we leave/skip it

Yes, the direct object is omitted because it is understood from context.

Hungarian often leaves out words that are obvious. Here, nem hagyjuk ki literally means:

• we do not leave it out
• we do not skip it

What it refers to depends on context, but most naturally it refers back to the round/lap/route.

So a fuller version could be something like:

• Akár rövid, akár hosszú a kör, nem hagyjuk ki a kört.

But that sounds repetitive, so Hungarian normally leaves the object unstated.

Yes, it is natural, especially if the context makes kör clear.

It has a very typical Hungarian structure:

• Akár X, akár Y... = whether X or Y...
• nem hagyjuk ki = we won’t skip it / we do not leave it out

A learner should mainly notice these natural patterns:

1. akár ... akár ... for whether ... or ...
2. omitted van in present tense
3. contrastive word order: hosszú a kör
4. separated verbal prefix after negation: nem hagyjuk ki
5. definite conjugation: hagyjuk

Only roughly. A word-for-word breakdown would be something like:

• Akár = whether
• rövid = short
• akár = whether/or
• hosszú = long
• a kör = the round/lap/route
• nem = not
• hagyjuk = we leave / we let
• ki = out

So very literally:

• Whether short, whether long the round, we do not leave out.

That is not good English, but it helps show the structure.

A natural English version would be:

• Whether the round is short or long, we don’t skip it.
• Whether it’s a short or long lap, we don’t leave it out.

Yes. Akár is a flexible word in Hungarian.

In other contexts it can mean things like:

• even
• up to / as much as
• part of expressions meaning any / whichever

For example:

• Akár holnap is mehetünk.
  = We could even go tomorrow.
• Akár tíz ember is eljöhet.
  = Even ten people may come / As many as ten people may come.

But in the pattern akár ... akár ..., the meaning is very clearly:

• whether ... or ...

So in your sentence, that is the meaning to focus on.