7. Tangents are drawn from point $A$ to a circle with a radius of 10 cm, touching the circle at points $B$ and $C$ such that triangle $A B C$ is equilateral. Find its area.
Solution: $\triangle A B C$ is equilateral, $A C, A B$ are tangents, $R=10, A B=$ ?

$\angle A C B=60^{\circ}, \angle A O C=90^{\circ}(A C \perp O C), \angle O C B=30^{\circ}$,

$B C=R \cos 30^{\circ} \cdot 2=R \sqrt{3}=10 \sqrt{3}, A B=B C=A C=10 \sqrt{3}$,

$S_{\triangle A B C}=\frac{A B^{2} \sqrt{3}}{4}=\frac{100 \cdot 3 \sqrt{3}}{4}=75 \sqrt{3}$.

Answer: $S_{\triangle A B C}=75 \sqrt{3}$.