The reactions of C3H and C4H radicals with C6H2 were investigated for the first time. Reactants C3H, C4H, and C6H2 were synthesized in two beams of C2H2 diluted with helium by pulsed high voltage discharge. We measured translational-energy distributions, angular distributions, and photoionization-efficiency spectra of C9H2 and C10H2 produced from the title reactions in a crossed molecular-beam apparatus using synchrotron vacuum-ultraviolet photoionization. The C3H (C4H) + C6H2 reaction releases 42% (33%) of available energy into the translational degrees of freedom of product C9H2 (C10H2) + H and scatters products into a nearly isotropic angular distribution. The photoionization-efficiency spectrum of C9H2 (C10H2) is in good agreement with that of C9H2 (C10H2) produced from the C7H (C8H) + C2H2 reaction. The ionization threshold, after deconvolution, was determined as 8.0 +/- 0.1 eV for C9H2 and 8.8 +/- 0.1 eV for C10H2. The combination of measurements of product translational-energy release and photoionization-efficiency spectra indicates productions of (HC9H)-H-3/c-(HC3)-H-1(C)C5H/c-(HC7)-H-1(C)CH + H and (HC10H)-H-1 + H in the two title reactions, which are supported also by quantum-chemical calculations. Ratios branching to the three isomers of C9H2 remain unknown. This work demonstrates that long carbon-chain molecules (e.g., C9H2 and C10H2) can be synthesized from reactions of CmH (e.g., m = 3 and 4) radicals with polyynes (e.g., HC6H) and gives some valuable implications to planetary, interstellar, and combustion chemistry.