Math 9 – Circle Geometry Take-Home Test
Name: __________________________________
Date: ____________________________________
Part 1: Matching (1/2 mark each)
/
Part 2: Written Response (1 mark each)
____
1) Tangents from an external point are
equal
____
2) A tangent is perpendicular to the
radius at the point of contact
a)
b)
c)
d)
e)
f)
g)
h)
3) The line joining the midpoint of the
chord to the centre is perpendicular
to the chord.
____
4) Central angles containing equal
chords or arcs are equal.
____
5) Inscribed angles containing the
same or equal chords or arcs are
equal.
____
____
6) The perpendicular bisector of a
chord passes through the centre of
the circle.
____
7) The line through the centre,
perpendicular to a chord, bisects
the chord.
____
8) Opposite angles of a cyclic
quadrilateral are supplementary.
____
9) An inscribed angle in a semicircle
measures
.
j)
i)
10) An inscribed angle equals half the
central angle containing the same
chord or arc, or an equal chord or
arc.
____
-
Answer each of the following.
Remember to put in your degree symbols.
1)
2)
x=
x=
3)
4)
m1 m2
VUT 
x=
QXR 
y=
5)
6)
x=
x=
y=
7)
8)
and
are
tangent lines
x=
PY 
9)
10)
is tangent to
the circle at the
point
a 
TOS 
RSU 
11)
12)
1 
a 
2 
b 
3 
4 
c 
5 
d 
13)
14)
AEF 
1 
BFE 
2 
DGE 
3 
15)
16)
1 
BDC 
2 
DCB 
3 
17)
DBC 
18)
XY 
4 
XA 
5 
6 
AB 
7 
19)
20)
3 
4 
4 
5 
21)
22)
6 
ABC 
7 
4 
8 
5 
23)
24)
4 
FEH 
5 
GEF 
EHG 
ABC 
Part 3: Application Problems (5 marks each):
- Work must be shown for full marks
1) A 20 cm cut is made 9 cm from the outside edge of a circle. What is the radius of the circle
(accurate to the nearest tenth.)
2) In the circle,
and
are parallel chords
apart. If
, then how far is
from the centre of the circle?
and