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
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '11
 cemtezer
 Geometry, radical axis

Click to edit the document details