Task B-3.3. In a circle, two diameters are drawn intersecting at an angle of $30^{\circ}$. The endpoints of these diameters determine two chords (different from the diameters) whose lengths differ by $2 \sqrt{2}$. What is the area of the circle?
Solution. Sketch...

![](https://cdn.mathpix.com/cropped/2024_05_30_0148fcdd1c92efebb536g-15.jpg?height=742&width=724&top_left_y=556&top_left_x=619)

Given is $t_{1}-t_{2}=2 \sqrt{2}$.

From $\sin 75^{\circ}=\frac{t_{1}}{2 r}$ we get $t_{1}=2 r \sin 75^{\circ}$, and from $\sin 15^{\circ}=\frac{t_{2}}{2 r}$ we get $t_{2}=2 r \sin 15^{\circ}$.

(1 point)

Substituting the obtained values into the given equation, we get

$$
r=\frac{\sqrt{2}}{\sin 75^{\circ}-\sin 15^{\circ}}=\frac{\sqrt{2}}{2 \cos 45^{\circ} \sin 30^{\circ}}=2
$$

Therefore, $P=4 \pi$.