# 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**

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?

- 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 - 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 - 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 2*x* - *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.

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## 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.