Angles in a Circle
What do we call an angle whose vertex lies on the circle, and whose sides are chords of the circle?
What is an Interior Angle
Chords AB and CD intersect inside circle Q at point P (not the center of the circle). If AP = 5, BP = 4, and CD = 12, what is the value of CP?
What is CP = 2 or 10.
What is the formula for calculating two secants inside the circle?
What is whole x outside = whole x outside
When a radius and a tangent line meet, they form what kind of angle?
What is Right Angle (90 degrees)
What is the formula for Arc Length?
What is L = (m/360) * 2πr, m is the central angle
If a central angle measures 50°, what is the measurement of its arc?
What is 50 degrees
Two chords intersect within a circle. On one chord, the segments have lengths of 4 cm and 8 cm. On the other chord, one segment has a length of 10 cm, and the other has a length of x cm. What is the value of x?
What is x = 3.2
If one whole secant measures 8 cm and the outside segment measures 3 cm, while the second whole secant measures 10 cm, and the outside segment measures X, what is the value of X?
What is X = 2.4
What can we use to prove that a line is indeed tangent to the circle?
What is the Pythagorean Theorem
(Or the slope formula)
If an arc has an arc measuring 30 degrees and a radius of 4 cm, what the Arc Length? round to the nearest tenth
What is 2.1 cm
If an inscribed angle measures 58°, what is the measure of its arc?
What is 116 degrees
What is the measure of the arc cut off by a chord 12 cm long in a circle of radius 10 cm?
What is 147.48 degrees
From a point outside a circle, a secant line is drawn with a total length of 4x and an external segment of length 2. A tangent line drawn from the same point has a length of 5. What is the value of x, rounded to 3 decimal places?
What is x = 3.125
Two circles have radii of 10 cm and 5 cm, and their centers are 25 cm apart. Find the length of the common internal tangent between these two circles.
What is 20 cm
An arc measures 140 degrees and has a radius of 5 feet. What is the Arc Length? round to the nearest tenth
What is 12.2 feet
If two chords intersect inside a circle, forming an angle that intercepts arcs of 120° and 40°, what is the measure of the interior angle?
What is 80 degrees
What is 2 rt (39) or 12.49
From a point outside a circle, two secant lines are drawn. The first secant has segments of length 9 (external) and 20 (internal). The second secant has an external segment of length 10 and an internal segment of length x. What is the value of x, rounded to the nearest tenth?
What is X = 16.1
Two tangent lines from an external point A touch a circle at points B and C. If the length of segment AB is 2x+3 and the length of segment AC is 5x−9, find the value of x and the length of the tangent segments.
What is x = 4 and AB = AC = 11 units
A circle has a shaded region with an arc of 127 degrees and a radius of 8 feet. What is the area of this sector? Round to the nearest WHOLE number
What is 71 feet squared.
Given an exterior angle with intercepted arcs of 103° and 68°, what is the measure of its supplementary angle?
What is 162.5 degrees.
In the center of a historic town square, there's a circular well with a diameter of 10 feet. A wooden plank is placed across the well, and the shortest distance from the center of the well to the plank is 3 feet. What is the length of the wooden plank (chord)?
What is 8
From a point outside a circle, two secant lines are drawn. The first secant has segments of length 8 (external) and 2 (internal). The second secant has an internal segment of length 11 and an external segment of length x. What is the value of x?
What is X = 5
Note: x = -16 is an extraneous solution
From an external point, two tangent lines are drawn to a circle. If the lengths of the tangent segments from the external point to the points of tangency are 30 cm and (3x−15) cm, what is the value of x?
What is X = 15
A large piece of pizza has an arc measure of 60 degrees and a side, or radius, that is 6 inches long. You decide to eat 3 pieces. What is the area of the pizza that you ate? Round to the nearest tenth.
What is 56.5 in. squared