12 multiple-choice questions, progressively harder.
A given circle has diameter 26 cm. What perimeter results when its inscribed regular hexagon is constructed by radius stepping?
Solution
Correct answer: B
The compass opening is half the diameter, and it becomes each hexagon side.
An equilateral triangle is constructed by alternate vertices of a hexagon in a circle of radius 4 cm. What is the perpendicular distance from O to a triangle side?
Correct answer: D
Half of a 120-degree center triangle has hypotenuse 4 cm. Its apothem is the shorter leg of a 30-60-90 triangle.
A square is constructed inside a circle of diameter 22 cm. What is its exact area?
Correct answer: A
The circle radius is 11 cm. The constructed square has area twice the squared radius.
A hexagon constructed in a given circle has radius 6.5 cm. What is its apothem?
Correct answer: C
Half a hexagon side is 3.25 cm. The apothem is the longer leg of its 30-60-90 right half-triangle.
ABCDEF is a radius-stepped regular hexagon in a given circle. What is angle ACD?
Three successive 60-degree center turns place D opposite A, so AD is a diameter. Angle ACD subtends that diameter and is a right angle.
A hexagon is constructed by stepping an 8 cm radius. What is the chord joining A to C, two steps later?
The center angle AOC is 120 degrees. Its perpendicular bisector creates two 30-60-90 right triangles, each with hypotenuse 8 cm.
A constructed regular hexagon has circumradius 11 cm. What is the perpendicular distance between two opposite parallel sides?
Each opposite side is one apothem from O, on a different side of the center. Add the two distances.
An alternate-vertex inscribed equilateral triangle has perimeter 45345\sqrt3453 cm. What compass opening produced the underlying radius-stepped hexagon?
Divide by three for a triangle side, then divide by the square root of 3 for the circle radius. That radius was the hexagon's compass opening.
An inscribed square constructed from perpendicular diameters has perimeter 12212\sqrt2122 cm. What is the radius of its given circle?
One square side is one fourth of the perimeter. A side is the radius times the square root of 2.
A radius-stepped hexagon has circle radius 20 cm. What is the area of one center triangle OAB?
OAB is equilateral with side 20 cm. Its altitude is 10 times the square root of 3 cm.
A hexagon and its alternate-vertex equilateral triangle are constructed in a circle of radius 10 cm. How much greater is the hexagon apothem than the triangle apothem?
The two apothems come from different right half-triangles, even though their radii agree. Subtract their lengths in the stated order.
A circular plaque has diameter 10 cm. A hexagon border and a square border can each be constructed inside it. How much more straight trim does the regular hexagon border require?
The common radius is 5 cm. Count six radius-length hexagon sides and four square sides of length 5 times the square root of 2 cm.
The difference is positive since 202<3020\sqrt2<30202<30.
Reset this practice set?
This clears every answer you have given and starts the set again from question 1.