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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.
$r=$
$8cm$
$4cm$
$2cm$
$12cm$
Question 3:
1 pts
Find the radius of the circle shown on the picture.
$r=$
$4\sqrt{3}cm$
$2\sqrt{3}cm$
$6\sqrt{2}cm$
$2\sqrt{2}cm$
Question 4:
1 pts
Find the missing value $x. $(the distance between the center of the circle and its chord)
$x=$
$4cm$
$6cm$
$6\sqrt{2}cm$
$4\sqrt{3}cm$
Question 5:
2 pts
Find the length of the chord $AB$ shown on the picture.
$AB=$
$9cm$
$9\sqrt{2}cm$
$6\sqrt{2}cm$
$4\sqrt{3}cm$
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$=$
$6cm$
$12cm$
$18cm$
$24cm$
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 $5 cm.$
$3$
$4$
$5$
$6$
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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