Ch. 12 Circles
12-1 Vocabulary
interior of a circleconcentric circlescongruent circles
exterior of a circletangent circlespoint of tangency
chordsecantcommon tangenttangent of a circle
The interior of a circleis the set of all points inside the circle. The exterior of a circleis the set of all points outside the circle.
Example 1: Identify each line or segment that intersects P.
Example 2: Find the length of each radius. Identify the point of tangency and write the equation of the tangent line at this point.
A common tangent is a line that is tangent to two circles.
Example 3: Early in its flight, the Apollo 11 spacecraft orbited Earth at an altitude of 120 miles. What was the distance from the spacecraft to Earth’s horizon rounded to the nearest mile?
Example 4: RS and RT are tangent to Q. Find RS.
12-2 Vocabulary
central angleminor arc semicirclecongruent arcs
arcmajor arc adjacent arcs
A central angleis an angle whose vertex is the center of a circle. An arcis an unbroken part of a circle consisting of two points called the endpoints and all the points on the circle between them.
Example 1: The circle graph shows the types of grass planted in the yards of one neighborhood. Find mKLF.
Adjacent arcs are arcs of the same circle that intersect at exactly one point. RS and ST are adjacent arcs.
Example 2:
Within a circle or congruent circles, congruent arcs are two arcs that have the same measure.
In the figure STUV.
Example 3: C J, andmGCD mNJM. Find NM.
Example 4: Find NP.
Convert each measure from degrees to radians.
85°90°
Convert each measure from radians to degrees.
***HW due Thursday 5/16***
12-1 Pg. 797 (1-3, 9 – 17 odd, 18 -22, 27, 31 -33) 12-2 Pg. 806 (1-4, 5 – 19 odd, 27 – 31, 39) Pg. 817 (1, 11 – 17 odd) + Circles Worksheet
12-7
12-3
Vocabulary
sector of a circle
segment of a circle
arc length
The area of a sector is a fraction of the circle containing the sector. To find the area of a sector whose central angle measures m°, multiply the area of the circle by
Example 1:
Find the area of each sector. Give answers in terms of and rounded to the nearest hundredth.
sectorHGJsector ABC
A segment of a circle is a region bounded by an arc and its chord.
Example 2: Find the area of segment LNM to the nearest hundredth.
Example 3: Find each arc length. Give answers in terms of and rounded to the nearest hundredth.
Arc FG
12-4
Vocabulary
inscribed angle
intercepted arc
subtend
An inscribed angleis an angle whose vertex is on a circle and whose sides contain chords of the circle.
An intercepted arcconsists of endpoints that lie on the sides of an inscribed angle and all the points of the circle between them.
A chord or arc subtendsan angle if its endpoints lie on the sides of the angle.
Example 1: Finding Measures of Arcs and Inscribed Angles. Find each measure mPRU and
Example 2: Hobby Application
An art student turns in an abstract design for his art project.
Find mDFA.
Example 3: Finding Angle Measures in Inscribed Triangles
Find aFind mLJM
Example 4: Finding Angle Measures in Inscribed Quadrilaterals
Find the angle measures of GHJK.
*** HW due Friday is 12-3 Pg. 813 (12 – 26 even) 12-4 Pg. 824 (13 – 27odd) + 2 & 3 below. ***
Find the equation of the line tangent to the given circle at the given point.
1. 2. 3.
12-5 and 12-6
Find mEFH
Find the value of x.
C.
Find mRNM
Find the value of x and the length of each chord.
The art department is contracted to construct a wooden moon for a play. One of the artists creates a sketch of what it needs to look like by drawing a chord and its perpendicular bisector. Find the diameter of the circle used to draw the outer edge of the moon.
A secant segmentis a segment of a secant with at least one endpoint on the circle. An external secant segmentis a secant segment that lies in the exterior of the circle with one endpoint on the circle.
Find the value of x and the length of each secant segment.
A tangent segmentis a segment of a tangent with one endpoint on the circle. AB and AC are tangent segments.
Find the value of x.