Собака бігає навколо дерева.

Because навколо normally requires the genitive case.

• дерево = nominative, the basic dictionary form, tree
• дерева = genitive singular, of a tree / around a tree in this context

So:

• навколо дерева = around the tree

This is very common in Ukrainian: certain prepositions force a particular case, and навколо is one of the prepositions that usually takes the genitive.

Grammatically, yes: собака is usually treated as a feminine noun because it ends in -а.

So in grammar:

• собака = feminine noun
• verbs in the present tense do not change for gender, so that does not affect бігає
• adjectives and past-tense verbs would agree with it as feminine

For example:

• велика собака = a big dog
• собака бігала = the dog was running / used to run

Even if the actual dog is male, собака is still often grammatically feminine. If you specifically want male dog, you can also use пес.

It can mean both, depending on context.

Ukrainian present tense often covers both:

• runs
• is running

So Собака бігає навколо дерева can mean:

• The dog runs around the tree
• The dog is running around the tree

Very often, бігає suggests repeated, ongoing, or habitual movement. If you want a more one-direction, right-now sense, learners often compare it with біжить.

This is a very common question.

• біжить = is running in a single instance, one current movement, more like is running now
• бігає = runs / is running around repeatedly / habitually / back and forth

So:

• Собака біжить до дерева = The dog is running to the tree.
• Собака бігає навколо дерева = The dog runs / is running around the tree, often with a sense of repeated or circular motion

In your sentence, бігає sounds natural because going around something suggests repeated movement rather than a single straight run.

A helpful approximate pronunciation is:

• бігає ≈ BEE-ha-ye

A few details:

• бі sounds like bee
• г in Ukrainian is usually pronounced like a softer h sound, not the hard English g
• ає at the end is pronounced roughly like a-ye

So the whole word is approximately BEE-ha-ye.

Because Ukrainian г is a different sound. It is usually pronounced more like a voiced h sound.

So:

• г in бігає is not the hard g of go
• it is closer to an h sound, though not exactly the same as English h

If you want the hard g sound in Ukrainian, the letter is ґ, but it is much less common.

So:

• г = softer, h-like sound
• ґ = hard g sound

Yes. Ukrainian has no articles.

English distinguishes:

• a dog
• the dog

Ukrainian usually just says:

• собака

The exact meaning depends on context. So Собака бігає навколо дерева could mean:

• A dog is running around a tree
• The dog is running around the tree

If the meaning has already been shown to the learner, context tells you which one is intended.

Yes. Ukrainian word order is more flexible than English word order.

The neutral order here is:

• Собака бігає навколо дерева.

But you may also see variations like:

• Навколо дерева бігає собака.
• Собака навколо дерева бігає.

These alternatives can shift emphasis or sound more marked. The original version is the most straightforward and natural for a basic statement.

Here навколо is a preposition, meaning around.

It introduces the phrase:

• навколо дерева = around the tree

You may also encounter навколо in related uses meaning around/about in a broader sense, but in this sentence it is simply a preposition of location or movement around something.

Because собака is the subject of the sentence, so it stays in the nominative case.

• собака = nominative singular
• it is the one doing the action

Meanwhile, дерева changes because it comes after навколо, which requires the genitive.

So the case pattern is:

• собака = nominative subject
• дерева = genitive after a preposition

бігає is third person singular present tense.

That means it corresponds to:

• he runs
• she runs
• it runs

In this sentence, it matches собака:

• собака бігає = the dog runs / is running

Some related forms are:

• я бігаю = I run
• ти бігаєш = you run
• він/вона бігає = he/she runs
• ми бігаємо = we run
• ви бігаєте = you run
• вони бігають = they run

It can express movement around something, so it is tied to the action of running.

In this sentence, the dog is not just located near the tree. The phrase shows the path of movement:

• the dog runs around the tree

So it is more dynamic than a simple location phrase like біля дерева (by the tree / near the tree).

Yes, often it would.

• собака = dog
• пес = dog, especially a male dog, and often feels a bit more specific

So:

• Пес бігає навколо дерева. = The dog is running around the tree.

Both are natural, but собака is a very common general word for dog.

A useful guide is:

• соба́ка
• бі́гає
• навко́ло
• де́рева

Stress matters in Ukrainian pronunciation, so learning it early is helpful. If you say the right vowels but stress the wrong syllable, people may still understand you, but it will sound less natural.