10.007. An isosceles trapezoid with a side length of 17 cm is circumscribed around a circle with a diameter of 15 cm. Find the bases of the trapezoid.
Solution.

According to the condition, $K Q=15 \mathrm{~cm}, A B=C D=17 \mathrm{~cm}, B C+A D=A B+C D=34$. In $\triangle C E D \angle C E D=90^{\circ}, C E=K Q$ (Fig. 10.7) We have $D E=\sqrt{289-225}=8 \mathrm{~cm}$, $A D=2 E D+B C=16+B C, B C+16+B C=34, B C=9 \mathrm{~cm}, A D=25 \mathrm{~cm}$.

Answer: 9 cm $; 25$ cm.