Quiz about Circles High School Geometry

Question 1

Quadrilateral $$A B C D$$ is inscribed in circle $$O$$, as shown. What is the value of $$y$$ ?

![](http://admin.getprephub.com/media/editor/gp6_20230225205418967266.png)

Accepted Answer

Covalent bond

Answer

$$97^{\circ}$$

Answer

$$77^{\circ}$$

Answer

$$47^{\circ}$$

Answer

$$107^{\circ}$$

Question 2

A circle with center $$O$$ is shown.

![](http://admin.getprephub.com/media/editor/gp14_20230225211045422824.png)
Create the equation for the circle.}

Accepted Answer

Covalent bond

Answer

$$(x-1)^{2}+(y-1)^{2}=16$$

Answer

$$(x+1)^{2}+(y+1)^{2}=16 $$

Answer

$$x^{2}+y^{2}=16$$

Answer

$$ x+y=16$$

Question 3

Which diagram shows only the first step of constructing the line perpendicular to $$\overline{A B}$$ through point $$P$$ ?

Accepted Answer

Covalent bond

Answer

![](http://admin.getprephub.com/media/editor/gp9s_20230225205645258986.png)

Answer

![](http://admin.getprephub.com/media/editor/gp9ss_20230225205659162010.png)

Answer

![](http://admin.getprephub.com/media/editor/gp9sss_20230225205722055958.png)

Answer

![](http://admin.getprephub.com/media/editor/gp9ssss_20230225205731754059.png)

Question 4

In the figure shown, $${L}$$ is the center of the circle and $$\overline{P Q}$$ is a chord of the circle measuring $$30$$ centimeters (cm).

![](http://admin.getprephub.com/media/editor/t1_20230225220149565923.png)
What is the length, in centimeters, of $$P L$$ ?

Accepted Answer

Covalent bond

Answer

17

Answer

34

Answer

8

Answer

15

Question 5

To estimate the area of the circle, Henry divides a circle of radius $$r$$ into $$n$$ triangles, as shown, and uses the expression $$\frac{h}{2}(b_1+b_2+b_3+b_4+\cdots . . b_n)$$ to estimate the area of the circle. In the expression, variables $$b_1, b_2$$ upto $$b_n$$ represent the base lengths of each triangle and $${h}$$ represents the height of each triangle.
![](http://admin.getprephub.com/media/editor/t8_20230225220534747391.png)
Henry claims that the more triangles the circle is divided into, the closer the estimated area will be to the actual area.

Which statement about Henry's claim is accurate?

Accepted Answer

Covalent bond

Answer

His claim is accurate because as $$n$$ gets larger, the value of $$h$$ gets closer to the value of $$r$$ and the value of $$(b_1+b_2+\cdots . . b_n)$$ approaches $$2 \pi r$$.

Answer

His claim is accurate because as $$n$$ gets larger, the value of $$h$$ gets closer to the value of $$2 r$$ and the value of $$(b_1+b_2+\cdots . . b_n)$$ approaches $$\pi r$$.

Answer

His claim is inaccurate because as $$n$$ gets larger, the value of $$h$$ gets closer to the value of $$r$$ and the value of $$(b_1+b_2+\cdots . . b_n)$$ deviates from $$2 \pi r$$.

Answer

His claim is inaccurate because as $$n$$ gets larger, the value of $$h$$ gets closer to the value of $$2 r$$ and the value of $$(b_1+b_2+\cdots . . b_n)$$ deviates from $$\pi r$$.

Ohio State Circles High School Geometry High School Geometry Maths Problems and Solutions

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