Hello, thesys!

If I understand the problem, there is an infinite number of answers.

I have two points $\displaystyle P$ and $\displaystyle Q.$

i need to find point $\displaystyle R$, defined by the intersection of $\displaystyle \overrightarrow{PR}$ and $\displaystyle \overrightarrow{QR}.$

The vectors are orthogonal, so that: .$\displaystyle \overrightarrow{PR}\cdot\overrightarrow{QR} \:=\:0$

How can i get the point $\displaystyle R$ ? Code:

* * * R
* o
* * *
* * *
*
* * *
P o - - - - * - - - - o Q

We have a semicircle with diameter $\displaystyle PQ.$

Let $\displaystyle R$ be *any* point on the semicircle.

Draw chords $\displaystyle PR$ and $\displaystyle QR.$

Then: .$\displaystyle PR \perp QR$