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A series of geometry problems focused on circles, tangents, and related theorems, along with their solutions. It covers topics such as common tangents, perpendicularity, arc measures, and secant relationships. The problems are designed to test understanding of geometric principles and problem-solving skills. It includes diagrams and step-by-step solutions, making it a useful resource for students studying geometry. The document also includes problems related to inscribed angles, diameters, and concentric circles, offering a comprehensive review of circle geometry.
Typology: Exams
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Given: Circle A externally tangent to Circle B.
A common internal tangent is:
line s
line r
segment AB - CORRECT ANSWER -Line r
Identify the common external tangent.
segment AB
line r
line s - CORRECT ANSWER -Line s
Given: Circle A externally tangent to Circle B.
Line segment AM is perpendicular to:
line segment MB
line r
line s
line segment JK - CORRECT ANSWER -Line R (definition of perpendicular)
Given: Circle A externally tangent to Circle B. The point of tangency of line s to circle A is _____.
point A
point M
point K
point J - CORRECT ANSWER -Point J
Given: Circle A externally tangent to Circle B. How many possible common tangents to circles A and B can exist?
4
3
2 - CORRECT ANSWER -3 (since one internal and two external tangents are possible)
Refer to the figure and match the theorem that supports the statement.
Given: Line segment PB is tangent.
Line segments PV, PU are secants.
If m arc VU = 80° and m arc ST = 40°, then m angle 1 =
Given: Line segment PB is tangent.
Line segments PV, PU are secants.
If m arc VU = 70° and m arc ST = 30°, then m angle 2 =
Given: Line segment PB is tangent.
Line segments PV, PU are secants.
If m arc VB = 60° and m arc BS = 30°, then m angle 3 =
Given: Line segment PB is tangent.
Line segments PV, PU are secants.
If m angle 1 = 30° and m arc ST = 20°, then m arc VU=
Given: Line segment AB diameter of Circle P.
If m angle 1 = 40°, then m arc AB=
Given: Line segment AD diameter of Circle P.
9 - CORRECT ANSWER -8 (since 10 x 4 is 40, 5 x X would need to equal 40 as well. Therefore 8. It is NOT addition, so NOT 9)
(Secant with an interior amount of 8, external amount of 4, and line x connected to it is shown) Find x in the given figures.
x = inches. - CORRECT ANSWER -I don't actually know this one cause I'm too lazy to figure it out, but 3√ is COMPLETELY wrong
(Two secant lines connecting, one with measurements of 5 (interior) and 4 (exterior), and another with measurements of x (interior) and 3 (exterior))
x =
6 9
12 - CORRECT ANSWER -
Find x in the given figure. (The vertical chord is a diameter.)
x = inches. - CORRECT ANSWER -2√
(Two secants (one a diameter) with both 30 and 10 degree angles, and an arc labeled x) x =
140
120 100 - CORRECT ANSWER -NOT 100, you just need to find the other two arcs above the diameter using the angle measurements, and subtract the combination of them by 180 to find x
(Square-ish shape inscribed in a circle, with bottom left corner equaling a 98 degree angle, with X in the top right corner --diagonally opposite) x =
262
98 82 - CORRECT ANSWER -82 (since the two combined angles would need to equal 180)
Given: Two concentric circles with center point P. How many tangent lines can be drawn that both circles share?
2 0
1 - CORRECT ANSWER -0 (a tangent cannot touch a circle at more than on point by definition, and concentric circles cannot therefore share a tangent)
