  We study the extreme value statistics of a run and tumble particle (RTP) in
one dimension till its first passage to the origin starting from the position
$x_0~(>0)$. This model has recently drawn a lot of interest due to its
biological application in modelling the motion of certain species of bacteria.
Herein, we analytically study the exact time-dependent propagators for a single
RTP in a finite interval with absorbing conditions at its two ends. By
exploiting a path decomposition technique, we use these propagators
appropriately to compute the joint distribution $\mathscr{P}(M,t_m)$ of the
maximum displacement $M$ till first-passage and the time $t_m$ at which this
maximum is achieved exactly. The corresponding marginal distributions
$\mathbb{P}_M(M)$ and $P_M(t_m)$ are studied separately and verified
numerically. In particular, we find that the marginal distribution $P_M(t_m)$
has interesting asymptotic forms for large and small $t_m$. While for small
$t_m$, the distribution $P_M(t_m)$ depends sensitively on the initial velocity
direction $\sigma _i$ and is completely different from the Brownian motion, the
large $t_m$ decay of $P_M(t_m)$ is same as that of the Brownian motion although
the amplitude crucially depends on the initial conditions $x_0$ and $\sigma
_i$. We verify all our analytical results to high precision by numerical
simulations.
