  The cluster structure of the neutron-rich isotope $^{10}$Be has been probed
via the $(p,p\alpha)$ reaction at 150 MeV/nucleon in inverse kinematics and in
quasifree conditions. The populated states of $^{6}$He residues were
investigated through missing mass spectroscopy. The triple differential
cross-section for the ground-state transition was extracted for quasifree angle
pairs ($\theta_{p}$, $\theta_{\alpha}$) and compared to distorted-wave impulse
approximation reaction calculations performed in a microscopic framework using
successively the Tohsaki-Horiuchi-Schuck-R\"opke product wave-function and the
wave-function deduced from Antisymmetrized Molecular Dynamics calculations. The
remarkable agreement between calculated and measured cross-sections in both
shape and magnitude validates the molecular structure description of the
$^{10}$Be ground-state, configured as an $\alpha$-$\alpha$ core with two
valence neutrons occupying $\pi$-type molecular orbitals.
