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• Geometry
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•  Question 1: 1 pts A quadrilateral is inscribed in a circle if and only if the opposite angles are supplementary.
•  Question 2: 1 pts Floor of a room is of dimensions $7 m \times 4 m$ and it is covered with circular tiles of diameters $10$ cm each as shown in the picture. We can find the area of floor that remains uncovered with the following expression. $$\left(7\cdot 4-28\cdot 5^{2}\pi\right)cm^{2}$$
•  Question 3: 1 pts ̉he area of the circle inscribed in a square of side $a cm$ is $\pi a^{2} cm^{2}$.
•  Question 4: 1 pts The perimeter of a square circumscribing a circle of radius$a cm$ is $8 a cm.$
•  Question 5: 2 pts Find $x$ and $y$ on the shown picture.
 $x=8^{\circ}, y=15^{\circ}$ $x=8^{\circ}, y=7^{\circ}$ $x=15^{\circ}, y=7^{\circ}$ $x=7^{\circ}, y=15^{\circ}$
•  Question 6: 2 pts The circumference of the circle described around the rectangle is $26\pi cm$. Find the area of that rectangle if his sides are in the ratio $5:12.$
 $A=5\cdot 24=120cm^{2}$ $A=12\cdot 20=240cm^{2}$ $A=15\cdot 8=120cm^{2}$ $A=10\cdot 24=240cm^{2}$
•  Question 7: 2 pts Find the length of the broken line shown on the picture. ($ABCD$ is rectangle)
The length of the broken line is $=$
•  Question 8: 2 pts Find the length of the broken line shown on the picture. ($ABCD$ is square)
The length of the broken line is $=$
•  Question 9: 3 pts Find the area of the circle inscribed in the rhombus shown on the picture
•  Question 10: 3 pts The following expression can be used to find the perimeter of the shaded area shown on the picture.$$4r^{2}=r^{2}+9\cdot 3 \Longrightarrow r=3cm$$ $$O=3\cdot(4+\pi)cm$$
•  Question 11: 3 pts In the following picture, a circle is inscribed in a square of side $5 cm$ and another circle is circumscribing the square. Is it true to say that area of the outer circle is two times the area of the inner circle?
•  Question 12: 3 pts Find the area of the flower bed (with semi-circular ends) shown on the picture.
$A=$