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.
 

Four Trapezia Formed by the Difference of Two Concentric Squares

Problem
ABCD is a square of side 10 cm. PQRS is a square inside ABCD. PQBA, QRCB, RSDC, and SPAD are identical trapezia, each of area 16 cm2. What is the height of each trapezium if PQ is parallel to AB and SR is parallel to DC?

A.   3 cm C.   2 cm
B.   1.8 cm D.   1.2 cm

 

2016-nov-math-trapezia_3d.jpg

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 cm2 C.   39.84 cm2
B.   52.05 cm2 D.   48.62 cm2

 

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