ところを見（み）ると is a set phrase in Japanese that highlights the situation or place of (A), before examining it subjectively. This often comes across simply as ‘judging from (A)’, or ‘seeing that (A)’. Literally, it can be thought of as ‘if looking at the aspect of (A)’, before the speaker will then go on to state what their judgment is.
This grammar pattern will appear directly following verbs in any of their standard forms.

• 彼（かれ）がニコニコしているところを見（み）ると、テストに合格（ごうかく）したに違（ちが）いない。
  Seeing that he is smiling, I have no doubt that he passed the test.
• 漢字（かんじ）を綺麗（きれい）に書（か）けるところを見（み）ると、彼（かれ）は長（なが）い間（あいだ）漢字（かんじ）を勉強（べんきょう）しているのかもしれない。
  Judging from the fact that he can write kanji very nicely, he probably has been studying kanji for a long time.
• 怒（おこ）られていてもずっと携帯（けいたい）を見（み）ているところを見（み）ると、彼（かれ）は全然（ぜんぜん）反省（はんせい）していないんだろう。
  Seeing that he is looking at his phone despite being scolded, he probably doesn’t feel any remorse.

Due to ところを見（み）ると expressing primarily subjective opions based on single observable actions, the (B) part of sentences including this structure will often include things like だろう, かも, でしょう, ね, etc, in order to show that the speaker is not actually claiming anything factually.