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  • Geometry
  • Circles
  • Application of Pythagorean Theorem to a Circle

Application of Pythagorean Theorem to a Circle

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  • Question 1:
    1 pts
    		The distance from the center of the circle with radius equal $5 cm$ to the chord of that circle is $3 cm.$ Find the length of the chord.
    $8cm$
    $4cm$
    $2cm$
  • Question 2:
    1 pts
    		Find the radius of the circle shown on the picture.
    $r=$
  • Question 3:
    1 pts
    		Find the radius of the circle shown on the picture.
    $r=$
  • Question 4:
    1 pts
    		Find the missing value $x. $(the distance between the center of the circle and its chord)
    $x=$
  • Question 5:
    2 pts
    		Find the length of the chord $AB$ shown on the picture.
    $AB=$
  • Question 6:
    2 pts
    		On the circle $k$ with diameter $|MN| = 25 cm$ lies point $J.$ Segment $|NJ|=7.$ Calculate the length of a segment $JM.$
    $12cm$
    $18cm$
    $24cm$
    $32cm$
  • Question 7:
    2 pts
    		In the circle with diameter $30 cm$ is constructed chord $18 cm$ long. Calculate the radius of a concentric circle that touches this chord.
    Radius$=$
  • Question 8:
    2 pts
    		The radius of circle $k$ measures $10 cm.$ Chord $GH = 12 cm.$ What is $TS?$
    $8cm$
    $4cm$
    $3cm$
    $2cm$
  • Question 9:
    3 pts
    		The radius of circle $k$ measures $4 cm.$ Find the length of the tangent segments from the point $P$ on the circle $k$ if the distance between the center of the circle and the point $P$ is $5 cm.$
  • Question 10:
    3 pts
    		In the circle there are two chord length $30$ and $34 cm.$ The shorter one is from the center twice than the longer chord. To determine the radius of the circle we can use the following expression $$r^{2}=15^{2}+\left(2x\right)^{2}\mbox{and } r^{2}=17^{2}+x^{2}$$ $$ 3x^{2}=64\Rightarrow x=\dfrac{8\sqrt{3}}{3}cm.$$

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