idioms - How to understand 節がある?

According to weblio, 節｛ふし｝がある is defined as follow:

着眼点としてある。そのようにも思われる。「思い当たるふしがある」や、「県警は当初、事件を隠蔽しようとしていたふしがある」などのように用いられる。

"Interesting" point. Considered to be like this. Used like 「思い当たるふしがある」 and 「県警は当初、事件を隠蔽しようとしていたふしがある」.

But I can't grasp what it would mean. 思い当たるふしがある is like "if someone mentions it that appears to be evident" and 「県警は当初、事件を隠蔽しようとしていたふしがある」 would maybe mean "At first, the police tried to keep the case secret". But I fail to get the nuances.

I have found a lot of examples here but I can't still make anything of it.

In particular,

頭と胴体と、強い方が相手を制するのではないかと思われるふしがある。

The combination 思われるふしがある makes little sense to me.

Could someone clarify a bit what it means? or how can it be reformulated?

Answer

I think this 節 is more or less interchangeable with ところ, and it vaguely refers to "something that catches one's eyes" or "something that reminds someone of something". I feel it tends to refer to something negative or suspicious.

Anyway, this phrase is idiomatic, and safe translations would simply be "It appears to me that ～", "It reminded me of ～". I feel 言われてみると ("now that you've mentioned") is not always important, and your last example can be translated simply as "It seems that the stronger one will win."