# If I have the following triangles in a circle can I draw any conclusion about their similarity?

I would need this for a proof.

I have a two circles intersecting at two points P and Q. We draw a segment between this two points and we draw a segment $$AB$$ which is perpendicular to $$PQ$$ and goes through P. Then we draw another segment $$UV$$ which goes through P and through a point $$U$$ in the first circle and $$V$$ in the second.

Can I say something about the following triangles that I drew in my image? Especially about their similarity?

I would only please need a hint, I want to solve this myself.

I thank everyone for help and am sorry for the not so good picture.

EDIT:I am looking for some similarity of UOP,AOQ,QHW and PHB. If there is any other way I can see them to find some similarity I would be thankful for a hint.

• Which triangles are you interested in? Please edit the question to tell us - don't clarify in comments. One suggestion: does the similarity look plausible to you if one of the circles is really large? Commented May 1, 2021 at 19:50

Hint: Angles that subtend the same arc are congruent so $$\angle U \cong \angle A$$ and $$\angle W \cong \angle B$$
• @vintagestyle: if you are talking about $PQ$ no, they would not be the same as circles have different radii Commented May 1, 2021 at 22:00
• I would need to prove something regarding expressing $UW$ depending on the cosine of the angle $HPB$. Would you have any advice, especially to which triangles I should examine. Or should I maybe ask this as a new question? Commented May 4, 2021 at 11:15