  KIC 7955301 is a hierarchical triple system with eclipse timing and depth
variations discovered by the Kepler mission. It is composed of a non-eclipsing
primary star at the bottom of the red giant branch on a 209-day orbit with a
K/G-type main-sequence inner eclipsing binary, orbiting in 15.3 days. This
system was noted for the large amplitude of its eclipse timing variations (4
hours), and the clear solar-like oscillations of the red-giant component,
including p-modes of degree up to l=3 and mixed l=1 modes. The system is a
single-lined spectroscopic triple. We perform a dynamical model by combining
the Kepler photometric data, eclipse timing variations, and radial-velocity
data obtained at Apache Point (ARCES) and Haute Provence (SOPHIE)
observatories. The dynamical mass of the red-giant is determined with a 2%
precision at 1.30 (+0.03,-0.02) solar mass. We perform asteroseismic modeling
based on the global seismic parameters and on the individual frequencies. Both
methods lead to a mass of the red giant that matches the dynamical mass within
the uncertainties. Asteroseismology also reveals the rotation rate of the core
(15 days), the envelope (150 days), and the inclination (75 deg) of the red
giant. Three different approaches lead to an age between 3.3 and 5.8 Gyr, which
highlights the difficulty of determining stellar ages despite the exceptional
wealth of available information. On short timescales, the inner binary exhibits
eclipses with varying depths during a 7.3-year long interval, and no eclipses
during the consecutive 11.9 years. This is why Kepler could detect its
eclipses, TESS will not, and the future ESA PLATO mission should. Over the long
term, the system owes its evolution to the evolution of its individual
components. It could end its current smooth evolution by merging by the end of
the red giant or the asymptotic giant branch of the primary star.
