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If be the centres of three co-axial circles and be the lengths of the tangents to…
MATHEMATICS · Subjective · ICSE · Mathematics · Geometry · Geometry
Problem
If
A
,
B
,
C
A, B, C
A
,
B
,
C
be the centres of three co-axial circles and
t
1
,
t
2
,
t
3
t_1, t_2, t_3
t
1
,
t
2
,
t
3
be the lengths of the tangents to them from any point, prove that
B
C
‾
⋅
t
1
2
+
C
A
‾
⋅
t
2
2
+
A
B
‾
⋅
t
3
2
=
0
\overline{BC} \cdot t_1^2 + \overline{CA} \cdot t_2^2 + \overline{AB} \cdot t_3^2 = 0
B
C
⋅
t
1
2
+
C
A
⋅
t
2
2
+
A
B
⋅
t
3
2
=
0
Related theory
Mathematical Logic
Power of a point
Circles
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