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  • Geometry
  • Circles
  • Circles and Quadrilaterals

Circles and Quadrilaterals

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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 7m×4m7 m \times 4 m and it is covered with circular tiles of diameters 1010 cm each as shown in the picture. We can find the area of floor that remains uncovered with the following expression. (7⋅4−28⋅52π)cm2\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 acma cm is πa2cm2\pi a^{2} cm^{2}.
  • Question 4:
    1 pts
    		The perimeter of a square circumscribing a circle of radiusacma cm is 8acm.8 a cm.
  • Question 5:
    2 pts
    		Find xx and yy on the shown picture.
    x=8∘,y=15∘x=8^{\circ}, y=15^{\circ}
    x=8∘,y=7∘x=8^{\circ}, y=7^{\circ}
    x=15∘,y=7∘x=15^{\circ}, y=7^{\circ}
    x=7∘,y=15∘x=7^{\circ}, y=15^{\circ}
  • Question 6:
    2 pts
    		The circumference of the circle described around the rectangle is 26πcm26\pi cm. Find the area of that rectangle if his sides are in the ratio 5:12.5:12.

    A=5⋅24=120cm2A=5\cdot 24=120cm^{2}

    A=12⋅20=240cm2A=12\cdot 20=240cm^{2}

    A=15⋅8=120cm2A=15\cdot 8=120cm^{2}

    A=10⋅24=240cm2A=10\cdot 24=240cm^{2}

  • Question 7:
    2 pts
    		Find the length of the broken line shown on the picture. (ABCDABCD is rectangle)
    The length of the broken line is ==
  • Question 8:
    2 pts
    		Find the length of the broken line shown on the picture. (ABCDABCD 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.4r2=r2+9⋅3⟹r=3cm4r^{2}=r^{2}+9\cdot 3 \Longrightarrow r=3cm O=3⋅(4+π)cmO=3\cdot(4+\pi)cm
  • Question 11:
    3 pts
    		In the following picture, a circle is inscribed in a square of side 5cm5 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=A=

Triangle

Quadrilateral

Circle

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