Understanding the users' performance for finding and selecting a target is important for designing an efficient user interface. However, little has been studied about the performance of screen reader users whose primary sense is audio. To better support touchscreen-based interaction for screen reader users, we conducted a user study on a smartphone with 12 participants with visual impairments where they were asked to perform a series of target acquisition tasks on a smartphone with screen reader on varying the screen size and the screen-Target ratio. As a result, we found that the participants were faster at finding targets with shorter traces when the screen size is smaller with larger target size in general. However, we also found that the ratio of the target size concerning the screen size affects task efficiency. In addition, we examined traces of touch events and identified five screen exploration strategies: zigzag, border-first, pigtail, hybrid, and other. Based on the findings, we suggest implications for designing an efficient touchscreen-based user interface for screen reader users.