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 STUV.

Example 3: C J, andmGCD  mNJM. 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 mPRU and

Example 2: Hobby Application

An art student turns in an abstract design for his art project.

Find mDFA.

Example 3: Finding Angle Measures in Inscribed Triangles

Find aFind mLJM

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 mEFH

Find the value of x.

C.

Find mRNM

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.