Given $A(0,2a),B(2b,0),C(0,0)$, then the midpoints are $(0,a),(b,a),(b,0)$. The line, through $C$ and $\bot AB\ :\ y=\frac{b}{a}x$ cuts $AB\ :\ y=-\frac{a}{b}(x-2b)$ in the point $D(\frac{2a^{2}b}{a^{2}+b^{2}},\frac{2ab^{2}}{a^{2}+b^{2}})$. Point $P(\frac{4a^{2}b}{a^{2}+b^{2}},\frac{4ab^{2}}{a^{2}+b^{2}})$. Condition $\Rightarrow \frac{4ab^{2}}{a^{2}+b^{2}}=a \Rightarrow a=\sqrt{3}b$. The angles are $30^{\circ}$ and $60^{\circ}$.