Download Geometry – Section 11.1 – Notes and Examples – Lines that

Geometry – Section 11.1 – Notes and Examples – Lines that Intersect Circles
Recall that a ________ is the set of all _________ in a plane that are ________________ from a given
_______, called the _________ of the circle. A _________ with __________ C is called circle C, or C.
The ___________ of a circle is the set of all points _________ the circle. The ____________ of a circle
is the set of all points __________ the circle.
A ___________ ___________ is a line that is tangent to _____ circles.
Problem 1
Identify each line or segment that intersects 𝑳.
Problem 2
Identify each line or segment that intersects 𝑷.
Problem 3
Find the length of each radius. Identify the point
of tangency and write the equation of the
tangent line at this point.
Problem 4
Find the length of each radius. Identify the point
of tangency and write the equation of the
tangent line at this point.
Problem 5
̅̅̅̅̅ and ̅̅̅̅̅
𝑯𝑲
𝑯𝑮 are tangent to 𝑭. Find 𝑯𝑮.
Problem 6
̅̅̅̅
𝑹𝑺 and ̅̅̅̅
𝑹𝑻 are tangent to 𝑸. Find 𝑹𝑺.
Geometry – Section 11.2 – Notes and Examples – Arcs and Chords
A __________ angle is an angle whose __________ is the _________ of a circle. An _____ is an
_____________ part of a circle consisting of _____ points called the ______________ and all the points
on the ________ between them.
________ arcs may be named by _____ points. ________ arcs and ________________ must be named
by ________ points.
_____________ arcs are arcs of the _______ circle that intersect at exactly
̂ and 𝑆𝑇
̂ are adjacent arcs.
_____ point. 𝑅𝑆
Within a circle or ______________ circles, ______________ arcs are _____ arcs
̂ ≅ 𝑈𝑉
̂.
that have the same measure. In the figure 𝑆𝑇
Problem 1
̂ and 𝒎𝑳𝑱𝑵
̂.
Find the measure of 𝒎𝑱𝑲𝑳
Problem 2
𝑪 ≅ 𝑱 and 𝒎∠𝑮𝑪𝑫 ≅ 𝒎∠𝑵𝑱𝑴. Find 𝑵𝑴.
Problem 3
Find 𝑵𝑷.
Problem 4
⃗⃗⃗⃗⃗⃗ bisects ∠𝑹𝑷𝑺. Find 𝑹𝑻.
𝑷𝑻
Problem 5
̂.
̅̅̅̅
𝑻𝑽 ≅ ̅̅̅̅̅
𝑾𝑺. Find 𝒎𝑾𝑺
Problem 6
̂.
̅̅̅̅. Find 𝒎𝑪𝑫
𝑨 ≅ 𝑩, and ̅̅̅̅
𝑪𝑫 ≅ 𝑬𝑭
Geometry – Section 11.3 – Notes and Examples – Sector Area and Arc Length
The ______ of a _________ is a fraction of the ________ containing the _________. To find the ______
𝑚°
of a sector whose central _______ measures 𝑚°, ___________ the area of the ________ by 360° .
A ____________ of a circle is a region ____________ by an _____ and its ________.
In a 30°-60°-90° ___________, the _________ of the leg ____________ the 60° ________ is √3 times
the _________ of the ___________ leg.
In the same way that the ______ of a _________ is a ___________ of the area of the ________, the
_________ of an _____ is a ___________ of the _____________________ of the circle.
Problem 1
Find the area of sector 𝑯𝑮𝑱. Give answers in
terms of .
Problem 2
Find the area of sector 𝑱𝑲𝑳. Give answers in
terms of .
Problem 3
A windshield wiper blade is 18 inches long. To the
nearest square inch, what is the area covered by
the blade as it rotates through an angle of 122°?
Problem 4
Find the area of segment 𝑹𝑺𝑻 to the nearest
hundredth.
Problem 5
̂ . Give answers in terms of 
Find the length of 𝑭𝑮
and rounded to the nearest hundredth.
Problem 6
̂ . Give your answer in
Find the length of 𝑮𝑯
terms of  and rounded to the nearest
hundredth.
Problem 7
Find the length of an arc with measure 135° in a
circle with radius 4 cm. Give your answer in terms
of .
Problem 8
Find the length of an arc with measure 62 in a
circle with radius 2 m. Give your answer in
terms of .
Geometry – Section 11.4 – Notes and Examples – Inscribed Angles
An ____________ angle is an angle whose __________ is on a _________ and whose sides contain __________
of the circle. An _______________ arc consists of ______________ that lie on the sides of an ____________
angle and all the points of the circle between them. A chord or arc _____________ an angle if its ____________
lie on the sides of the angle.
Problem 1
̂.
Find each measures of 𝒎∠𝑷𝑹𝑼 and 𝒎𝑺𝑷
Problem 2
̂ and 𝒎∠𝑫𝑨𝑬.
Find the measures of 𝒎𝑨𝑫𝑪
Problem 3
Find a.
Problem 4
Find 𝒎∠𝑳𝑱𝑴.
Problem 5
Find 𝒎∠𝑬𝑫𝑭.
Problem 6
Find the angle measures of GHJK.
Geometry – Chapter 11 – Section 5 – Notes and Examples
Problem 20
Find each measures of mEFH and mGF.
Problem 21
Find the measures of mSR and mSTU.
Problem 22
Find mAEB.
Problem 23
Find mABD.
Problem 24
Find mRNM.
Problem 25
Find the value of 𝒙.
Problem 26
Find mYZ.
Problem 27
Find mLP
U
U
V
V
Geometry – Chapter 11 – Section 6 – Notes and Examples