In this paper we study a partial differential equations model for tumour growth taking into account drug resistance. It is well known that angiogenesis, the process of creation of new blood vessels from existing ones, is induced by tumour cells to get the amount of nutrients and oxygen needed to continue their proliferation when the tumour has reached a critical size. Angiogenesis is therefore a target for therapy. The model we study takes into account two kinds of treatments: a cytotoxic treatment and a treatment which is both cytotoxic and anti-angiogenic. It is based on mass-balance equations on cells densities coupled with a diffusion equation for the nutrients and oxygen concentration. In a first part we prove that the model is well-posed if the initial tumour is compactly supported in the domain, which is the case for tumour metastases. The proof states that the tumour remains compactly supported in a finite time. In the model, we also consider the presence of a necrotic compartment composed of dead cells. Since some tumours can present necrosis while other do not, we want a model which can reproduce these two different cases. The second part of this paper is devoted to an asymptotic analysis which proves that the absence of necrosis is the limit case of our model when the necrosis is immediately evacuated.