Areas
The area of a rhombus is 64 in². One diagonal is half the length of the other. What are the lengths of the diagonals?
8 inches and 16 inches
What is the arc length of a circle with radius 6 cm and central angle 60°?
Answer: 2π
What is the image of the point (2, 3) after translating it 4 units right and 1 unit down?
Answer: (6, 2)
A circle has a circumference of 12pi. What is its diameter?
12
What is a chord?
A line segment with endpoints on a circle.
Find the area of a parallelogram if its length is 4 cm and its width is 10 cm.
40 cm²
What is the arc length of a circle with radius 8 cm and central angle 3π/4 radians?
6π
What is the image of the point (1, 2) after rotating it 90° counterclockwise about the origin?
Answer: (-2, 1)
A circle is inscribed inside a square with side length 8 units. What is the circumference of the circle? Explain how you know.
8pi
What is a diameter?
A chord that passes through the center of the circle.
Find the area of a circle if its diameter is 12 inches.
36π in²
A circle has circumference 20π cm. Find the arc length for a 72° central angle.
4π
What is the image of the point (3, -2) after reflecting it over the x-axis?
Answer: (3, 2)
Two circles have radii in a ratio of 2:5. What is the ratio of their circumferences?
2:5
What is the chord is bisected (cut into two equal parts)?
This happens when a radius is perpendicular to a chord.
Find the area of a trapezoid if the first base is 9 inches, the second base is 12 inches, and the height is 10 inches.
105 in²
A sector has an arc length of 12π cm and a central angle of 2π/3 radians. Find the radius.
18cm
What is the image of the point (2, 5) after a dilation from the origin with a scale factor of 2?
Answer: (4, 10)
A student claims: "If you increase the diameter of a circle by 4 units, the circumference also increases by 4л." Is the student correct?
Yes, the student is correct.
What is they are equidistant from the center?
If two chords are equal in length, this is true about their distance from the center.
The height of a triangle is 7 inches more than its base. If the area of the triangle is 60 in², find the base and height.
Base = 8 in, Height = 15 in
A runner travels along an arc of a circle with radius 50 m and covers an arc length of 25π m. Find the central angle in degrees.
90 degrees
What is the image of the point (-4, 1) after reflecting it over the y-axis and then translating it up 3 units?
Answer: (4, 4)
Explain why the ratio a is constant for all circles.
All circles are similar figures, meaning their shapes are identical regardless of size. When a circle is scaled up or down, both the circumference and diameter scale by the same factor.
Because they grow proportionally, the ratio 4 stays constant, which is defined as n.
What is equal? (product of one chord’s segments equals the product of the other)
When two chords intersect inside a circle, the products of their segments are…