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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 $$r^{2}=15^{2}+\left(2x\right)^{2}\mbox{and } r^{2}=17^{2}+x^{2}$$ $$3x^{2}=64\Rightarrow x=\dfrac{8\sqrt{3}}{3}cm.$$