11. Triangle $ABC$ has sides $\sqrt{3}$, $6$, and $\alpha$ (with the angle between them being $\alpha$) and is inscribable in a circle. If the area of this triangle is at most $4.5$, what is the minimum value of $\alpha$?
(1) $2$ (2) $3$ (3) $4$ (4) $5$
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31. Among triangles with area 35 square units that have a side of length 15 units in common, what is the minimum perimeter?

• [(1)] $30$
• [(2)] $32$
• [(3)] $34$
• [(4)] $36$

11. Tangent at a point of the ellipse $x ^ { 2 } / a ^ { 2 } + y ^ { 2 } / b ^ { 2 } = 1$ is drawn which cuts the coordinate axes at $A$ and $B$. The minimum area of the triangle $O A B$ is ( $O$ being the origin) :
(a) $a b$
(b) $\left( a ^ { 3 } + a b + b ^ { 3 } \right) / 3$
(c) $a ^ { 2 } + b ^ { 2 }$
(d) $\left( \left( a ^ { 2 } + b ^ { 2 } \right) \right) / 4$