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See the image. The white Circle and Line and X along the Line are your initial fixed elements.
Draw a Circle [the green one] with the 2P option, with the 1st point being the left quadrant point of the white Circle, and the 2nd point to the right of there by [since the 2P option defines a diameter] twice your specific radius. The desired-result Arc will be a portion of that green Circle. You're going to rotate the green Circle with the center of the white Circle as the rotation base point, so that at any rotation, it will always be tangent to the white Circle.
To determine the rotation: Draw a Circle [the yellow one] with its center at the center of the white Circle, and going through the X spot. Rotate the green Circle, giving it the center of the white Circle as the rotation base, and using the Reference-direction option. For the Reference [starting] direction, use from the center of the white Circle to the intersection of the yellow and green Circles [the blue Line], and for the new direction, the X spot [the magenta Line].
Use the white Circle and Line as trimming boundaries to Trim the rotated green Circle to the desired-result Arc [the red one].