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Problems in Geometry
(6)
1.
What is the locus of a point whereof the power with respect to a ﬁxed circle is a
constant ?
2.
Compute the power of the point
P
(
x
0
,y
0
) with respect to the circle
x
2
+
y
2
+2
ax
+2
by
+
c
= 0
.
Write down the equation of the radical axis of the circles
x
2
+
y
2
+2
a
1
x
+2
b
1
y
+
c
1
= 0
and
x
2
+
y
2
+ 2
a
2
x
+ 2
b
2
y
+
c
2
= 0
.
3.
Consider ﬁxed nonconcentric circles Γ
1
,
Γ
2
.
Prove that the locus of a point whereof
the powers with respect to Γ
1
and Γ
2
diﬀer by a constant is a line parallel to the radical
axis of Γ
1
and Γ
2
.
4.
Prove that the locus of a point whereof the ratio of powers with respect to two given
circles Γ
1
,
Γ
2
is a constant is a circle the centre of which lies on the line joining centres of
Γ
1
,
Γ
2
.
5.
Given two orthogonal circles, is it possible for the centre of one to lie on the other ?
6.
Let each one of the circles
C
1
, C
2
intersect each one of the circles Γ
1
,
Γ
2
orthogonally.
Prove that the radical axis of
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This note was uploaded on 11/14/2011 for the course MATH 373 taught by Professor Cemtezer during the Spring '11 term at Middle East Technical University.
 Spring '11
 cemtezer
 Geometry

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