Chords and Arcs
True or False: A chord always intercepts the center of the circle.
What is false?
How do tangents relate to the circle?
What is perpendicular to their radii?
If the right side of the circle's equation is equal to 64 mm, what is the radius of the circle?
8 mm
What abbreviations can be used to remember how to find sine, cosine, and tangent?
What is SOH CAH TOA?
What does Csc stand for?
What is cosecant?
If two chords in the same circle are congruent, the arcs that form from the chords' endpoints are...
What is congruent?
Give me a definition of a tangent.
What is a line that touches a circle at exactly one point but never enters the circle?
In the equation (x-5)2 + (y+7)2 = 4, what is a coordinate pair located on the circle?
What is (5, -7)?
What are the formulas for sine, cosine, and tangent?
sine: opp/hyp
cosine: adj/hyp
tangent: opp/adj
What are the formulas of cosecant, secant, and cotangent?
What are:
Cosecant: 1/sin(x)
Secant: 1/cos(x)
Cotangent: cos(x)/sin(x)
What fraction will you multiply to the circumference equation to find the length of a 60 degree arc on that circle?
What is 1/6?
Two tangents that share a common endpoint form a quadrilateral with two radii in a circle. The measure of the arc is 129 degrees. What is the measure of the angle formed by the two tangents?
What is 51 degrees?
What is the equation of a circle?
What is (x-h)2 + (y-k)2 = r2?
If you know the height of a tree, the distance a person is away from the tree, and the angle at which the person sees the top of the tree, which trigonometric function can be found with only that information?
What is tangent?
If sin θ = 0.5, then what is csc θ?
What is 2?
Two chords, AB and CD, are equidistant from the center of the same circle. The midpoint of chord AB is labeled E, and the midpoint of CD is labeled F. The length of AE is 4. What is the length of CD?
What is 8?
The radius of a circle is 3. The measure of segment AB laying on a tangent of a circle is 8, and the intersection of the segment and the circle is its midpoint. What is the distance of point A to the center of the circle?
What is 5?
Write the equation for a circle that has a diameter of 10 mm and a point on the circle located at (-3, 5).
What is (x+3)2 + (y-5)2 = 25?
If sin(x) = 0.5 and cos(y) = 0.5, what are the values of x and y?
What are 30 and 60 degrees (in that order)?
Which trig function(s) (sine/cosine/tangent) is used in cotangent?
What are sine and cosine?
Find the length of the arc that has a measure of 120 degrees in a circle with a radius of 9 mm in terms of pi.
What is 6 times pi?
Three segments, AC, DF, and GJ, land on tangents of the same circle, and they create a triangle. Points B, E, and H, respectively, are the midpoints of the segments, as they mark the intersection of the tangent to the circle. The measure of EF is equal to 7. What is the perimeter of the triangle formed?
What is 42?
Find the radius of the circle with the equation below:
x2+y2-4x+10y+4 = 0
What is 5?
DAILY DOUBLE:
What is the value of tan(tan(tan(tan(tan(tan(cos(90)?
What is 0?
What information can you find if you know the cosine of x, the measure of x, the length of the hypotenuse, and the length of the side opposite to angle x?
What is sine, cosine, cosecant, secant, and cotangent?