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  • Geometry
  • Circles
  • Triangles and Circles

Triangles and Circles

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  • Question 1:
    1 pts
    		Each of the two triangles is isosceles, $\vartriangle ABC$ and $\vartriangle ACD.$
  • Question 2:
    1 pts
    		Find the radius of the circle in this $5, 12, 13$ right triangle.
    Radius $=$
  • Question 3:
    1 pts
    		Find the perimeter of the shaded area shown on the picture.($\vartriangle ABC$ is an equilateral triangle.)
    $P=6\pi$
    $P=12\pi$
    $P=18\pi$
    $P=9\pi$
  • Question 4:
    1 pts
    		Find the perimeter of the shaded area shown on the picture.($\vartriangle ABC$ is an equilateral triangle.)
    $P=5\pi$
    $P=10\pi$
    $P=15\pi$
    $P=20\pi$
  • Question 5:
    2 pts
    		An equilateral triangle is inscribed in a circle. If the radius of the circle is $3\sqrt{3}cm$, which expression can be used to find the length of the side $a$ of the triangle?
    $a=\dfrac{3\cdot 3}{3}cm$
    $a=\dfrac{3\cdot 3\sqrt{3}}{\sqrt{3}}cm$
    $a=\dfrac{3\cdot 3\sqrt{6}}{\sqrt{3}}cm$
    $a=\dfrac{3\cdot 3\sqrt{3}}{\sqrt{6}}cm$
  • Question 6:
    2 pts
    		What is the area of a circle which is inscribed in a equilateral triangle of side $7cm$?

    $A=\dfrac{51}{15}\pi cm^{2}$

    $A=\dfrac{48}{13}\pi cm^{2}$

    $A=\dfrac{49}{12}cm^{2}$

    $A=\dfrac{49}{12}\pi cm^{2}$

  • Question 7:
    2 pts
    		Find the area of the right triangle shown on the picture.
    $A=$
  • Question 8:
    2 pts
    		Find the area of the shaded figure shown on the picture.
    $A=$
  • Question 9:
    3 pts
    		An equilateral triangle is inscribed in circle. Find the length of the longer arc $BC$ if the length of side of the triangle is $6cm.$
    $\dfrac{8\sqrt{3}}{3}\pi cm$
    $\dfrac{6\sqrt{3}}{5}\pi cm$
    $\dfrac{2\sqrt{3}}{3}\pi cm$
    $\dfrac{3\sqrt{3}}{2}\pi cm$
  • Question 10:
    1 pts
    		Area of triangle $=\dfrac{1}{2}\cdot a\cdot r +\dfrac{1}{2}\cdot b\cdot r+\dfrac{1}{2}\cdot c\cdot r=\dfrac{(a+b+c)}{2}\cdot r $
  • Question 11:
    3 pts
    		$AB$ is a diameter of the circle, $AC = 6 cm$ and $BC = 8 cm. $Find the area of the shaded regio.
    $A=(25\pi-16) cm^{2}$
    $A=(36\pi-25) cm^{2}$
    $A=(25\pi-24) cm^{2}$
    $A=(24\pi-25) cm^{2}$
  • Question 12:
    3 pts
    		In the given pictures, arcs have been drawn with radii $14 cm$ each and with centres $P, Q$ and $R.$ Find the area of the shaded region.
    $A=98\pi cm^{2}$
    $A=89\pi cm^{2}$
    $A=969\pi cm^{2}$
    $A=196\pi cm^{2}$

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