Does the radius of the quadrant pass from the center of the inscribed circle?

Notice that a tangent line passing through the point $T$ is tangent to both the quarter circle and the inscribed circle. That means the radii of the inscribed circle and the quarter circle are both perpendicular to the tangent line passing through the point $T$. That means the radius of the inscribed circle coincides with the radius from the quarter circle.

The great and the small circles have a common tangent in $T$ , so the orthogonal to this tangent passes through $P$ and $O$.