# Plane Geometry

## Radius of Circle of New Atom Smasher

**Problem**

A new kind of atom smasher is to be composed of two tangents and a circular arc which is concave toward the point of intersection of the two tangents. Each tangent and the arc of the circle is 1 mile long, what is the radius of the circle? Use 1 mile = 5280 ft.

A. 1437 ft. | C. 1347 ft. |

B. 1734 ft. | D. 1374 ft. |

## Regular Octagon Made By Cutting Equal Triangles Out From The Corners Of A Square

**Problem**

A regular octagon is made by cutting equal isosceles right triangles out from the corners of a square of sides 16 cm. What is the length of the sides of the octagon?

A. 6.627 cm | C. 6.762 cm |

B. 6.267 cm | D. 6.276 cm |

## Smallest Part From The Circle That Was Divided Into Four Parts By Perpendicular Chords

**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.

## Area Bounded by Intersecting Chords in a Circle

**Problem**

Chords *AB* and *CD* intersect each other at *E* inside the circle. *AE* = 8 cm, *CE* = 12 cm, and *DE* = 20 cm. If *AB* is the diameter of the circle, compute the area of *AEC*.

A. 61.04 cm^{2} |
C. 39.84 cm^{2} |

B. 52.05 cm^{2} |
D. 48.62 cm^{2} |