10.090. The distance from the center of the circle to a chord of length 16 cm is 15 cm. Find the area of the triangle circumscribed around the circle, if the perimeter of the triangle is $200 \mathrm{~cm}$.
## Solution.

Radius of the circle from $\triangle O C B: R=\sqrt{15^{2}+8^{2}}=17$ (cm). The required area of the triangle $S_{\triangle D K L}=R \cdot p=17 \cdot \frac{200}{2}=1700$ (cm²) (Fig. 10.87).

Answer: $1700 \mathrm{~cm}^{2}$.