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Math 12 Advanced
Circle Geometry Exam Review
Distance, Midpoint and Slope:
1. Determine the length, the midpoint and the slope of AB given A(3, -6) and B(-1, 10)
2. If A(-8, 5) is one endpoint and C(3, -1/2) is the midpoint, determine the coordinates of the other
endpoint B.
3. Determine the equation of the perpendicular bisector of chord AB given A(-5, 1) and B(2, -2). Could
the point (-3, -4) be the center of the circle? Explain.
4. Given AB is the diameter of a circle with A(6, 5) and B(7, -2). Is the point D(3, -1) inside, outside or
on the edge of the circle? Provide proof!
5. a) A chord 8 cm long is 3 cm from the center, what is the diameter of the circle?
b) A circle has a radius of 13 cm. Determine the distance between two parallel chords measuring 24 cm
and 10 cm respectively.
6. Prove the line segment joining the midpoints of AB and AC is parallel to and ½ the measure of side
BC in triangle ABC given A(4, -8), B(-2, 2) and C(12, 6).
7. A rectangle is given by the vertices R(-6,5), S(12,-1), T(8,-13), and U(-lO,-7). Show that the diagonals
bisect each other.
8. The vertices of an isosceles triangle are given by A(1,7), B(-5,1) and C(7,1). Determine whether the
triangle formed by joining the midpoints of the sides of ΔABC is also isosceles.
Angles and Arcs
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Angles inscribed from the same chord are the same measure
A central angle is twice the measure of an inscribed angle from the same chord
An angle subtended from the diameter measures 90 degrees
Opposite angles in a cyclic quadrilateral add up to 180 degrees
Measure of an arc is equal to the measure of the central angle subtended by the same chord
9. Determine measure of the indicated variables and measure of all arcs in the last two circles.
a)
y
x
b)
c)
x

y
130
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A
A
d)
40
y
z
B
35
95
z
E
78
x
D
Arc AB = 110
B
C
Circle and Ellipses
10. Which of the following is the circle and which is the ellipse – why? Rewrite each of the following in
transformational form.
a) 2 x 2  2 y 2  12 x  4 y  12  0
b) 16 x 2  9 y 2  64 x  54 y  1  0
c) Determine the center, the radius (major or minor axis) domain, range and mapping rule of (a) and (b).
 x  5   y  1
11. Rewrite in general form: 

 1
 3   2 
2
2
12. Generate an equation for an ellipse in transformational form given: ( x, y)  7 x  2, 12 y  3
Converse Statements:
Statement: If A, then B.
Converse: If B, then A.
If Both True: A iff B or B iff A
Geometric Proofs: SSS SAS ASA AAS HL (BUT NOT ASS)
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CPCTC – congruent parts of congruent triangles are congruent
Segment addition/segment subtraction
Angle addition/ angle subtraction
Collinear
Construction
1. Given: AD and BE bisect each other.
Prove: AB  DE
2.
3. Given: AE bisects BAC , AB  AC
Prove: 1  2
5. Given: D is the midpoint of CE .
AC  AE, AB  AF , C  E
Given: AB  AC , AD  AE
Prove: ABE  ACD
4. Given: 1  2, FE  AC , EB  FD
Prove: B  D
6. Given: AB  BC , CD  BC , BA  CD
Prove: BCA  CBD
Prove: BD  FD
7. Given: 1  2, BC  DE , B  E
Prove: BDA  ECA
8. Given: AB  BE , EF  BE , BC  DE , AD  CF
Prove: A  F