Circle

Problem
Calculate the area enclosed by the curve $x^2 + y^2 - 10x + 4y - 196 = 0$.

A.   15π C.   169π
B.   13π D.   225π

 

Problem
A circle has an equation of $x^2 + y^2 + 2cy = 0$. Find the value of $c$ when the length of the tangent from (5, 4) to the circle is equal to one.

A.   5 C.   3
B.   -3 D.   -5

 

Problem
What is the equation of the normal to the curve $x^2 + y^2 = 25$ at (4, 3)?

A.   $4x + 3y = 0$ C.   $3x + 4y = 0$
B.   $3x - 4y = 0$ D.   $4x - 3y = 0$

 

Problem
What is the radius of the circle $x^2 + y^2 - 6x = 0$?

A.   6 C.   4
B.   9 D.   3

 

Problem
Which of the following pizzas is a better buy: a large pizza with 16-inch diameter for \$15 or a medium pizza with an 8-inch diameter for \$7.50? What is the cost per square inch of the better pizza?

A.   medium pizza: \$0.07/in.2 C.   medium pizza: \$0.15/in.2
B.   large pizza: \$0.07/in.2 D.   large pizza: \$0.15/in.2

 

Situation
If a chord is selected at random on a fixed circle what is the probability that its length exceeds the radius of the circle?

  1. Assume that the distance of the chord from the center of the circle is uniformly distributed.
    A.   0.5 C.   0.866
    B.   0.667 D.   0.75
  2. Assume that the midpoint of the chord is evenly distributed over the circle.
    A.   0.5 C.   0.866
    B.   0.667 D.   0.75
  3. Assume that the end points of the chord are uniformly distributed over the circumference of the circle.
    A.   0.5 C.   0.866
    B.   0.667 D.   0.75

 

Problem
Divide the circle of radius 13 cm into four parts by two perpendicular chords, both 5 cm from the center. What is the area of the smallest part.
 

01 - Circle tangent to a given line and center at another given line

Problem 1
A circle is tangent to the line 2x - y + 1 = 0 at the point (2, 5) and the center is on the line x + y = 9. Find the equation of the circle.
 

The Circle

Definition of circle
The locus of point that moves such that its distance from a fixed point called the center is constant. The constant distance is called the radius, r of the circle.
 

09 Dimensions of smaller equilateral triangle inside the circle

Problem
From the figure shown, ABC and DEF are equilateral triangles. Point E is the midpoint of AC and points D and F are on the circle circumscribing ABC. If AB is 12 cm, find DE.
 

Two equilateral triangles inside a circle

 

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