Definitions and Properties
A line segment that has both endpoints on the circle.
What is a chord?
If a diameter or radius is perpendicular to a chord, then it does what to the chord?
It bisects it (splits it in half)
An inscribed angle has a vertex on the ________ with two sides that are _________.
Circle, chords.
We measure arc length in _______________.
Units of measurement.
How do you go from an inscribed angle measure to an arc measure?
You multiply the angle measure by two.
If two congruent arcs have two congruent chords and one chord equals 15m, what is the length of the other chord?
15 meters.
If the measure of an inscribed angle is 65 degrees, what is the measure of the corresponding arc?
Arc = 130 degrees
What is the equation for finding arc length?
How do you go from an arc measure to an inscribed angle?
You divide the measure by two.
If two congruent chords have two congruent arcs and one arc measures 18x-11 and the other arc measures 12x+25, what is the value of x?
x = 6.
If two inscribed angles intercept the same arc, the angles are _________.
Congruent
In Circle Y, the radius is equal to 6cm and the arc degree measure if 118 degrees. What is the arc length? Round to the nearest tenth.
12.4 cm.
Two chords are congruent only if...
Their corresponding arc are congruent.
Radius PQ is perpendicular to chord AB and bisects it at point C. The length of AC equals 7. What is the length of CB?
CB = 7.
Find the measure of the inscribed angle with a missing arc measure if the surrounding arcs add up to 270 degrees.
Angle = 45 degrees.
In Circle H, the diameter is 26ft and the arc degree measure is 98 degrees. What is the arc length? Round your answer to the nearest tenth.
144.5 ft.
If an inscribed angle intercepts a diameter, then it creates what kind of angle?
A right angle.
Diameter FG is perpendicular to chord BD and bisects it at point I. If the length of BI = 2x and the length of ID = x+12, find x and the length of BD.
x = 12
BD = 48 units
Find x if the angle measure is 4x -16 and the corresponding arc is 80 degrees.
x = 14
In Circle T, the radius is 15km and the surrounding arc measures add up to 215 degrees but you are missing the arc you are looking for. What is the arc length for the missing arc? Round to the nearest hundredth.