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Show that the length of the tangent from any point on the circle to the circle is .
MATHEMATICS · Subjective · ICSE · Mathematics · Geometry · Geometry
Problem
Show that the length of the tangent from any point on the circle
x
2
+
y
2
+
2
g
x
+
2
f
y
+
c
=
0
x^2 + y^2 + 2gx + 2fy + c = 0
x
2
+
y
2
+
2
g
x
+
2
f
y
+
c
=
0
to the circle
x
2
+
y
2
+
2
g
x
+
2
f
y
+
c
1
=
0
x^2 + y^2 + 2gx + 2fy + c_1 = 0
x
2
+
y
2
+
2
g
x
+
2
f
y
+
c
1
=
0
is
(
c
1
−
c
)
\sqrt{(c_1 - c)}
(
c
1
−
c
)
.
Related theory
Power of a point
Circles
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