6. Two circles of radii $R$ and $R^{\prime}$ touch each other externally at point $P$ and touch the line $l$ at points $A$ and $B$, respectively. Let $Q$ be the point of intersection of the line $B P$ with the first circle. Determine the distance from the line $l$ to the point $Q$.

![](https://cdn.mathpix.com/cropped/2024_05_06_bdfe3271f0fede0d79bbg-3.jpg?height=505&width=805&top_left_y=433&top_left_x=274)
Answer: $2 R$, i.e., this point is diametrically opposite to point $A$.

Solution: By drawing the common tangent at point $P$, we notice that in triangle $A P B$, angle $A P B$ is equal to the sum of the other two angles. Therefore, it is a right angle, and point $Q$ is diametrically opposite to point $A$.