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Byju's Answer
Standard IX
Mathematics
Every Point on the Bisector of an Angle Is Equidistant from the Sides of the Angle.
Find the circ...
Question
Find the circumcentre of the triangle with the vertices A (-3,4) , B (3,4) and C (-4,-3). What is the circumradius of the circle?
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Solution
We want the equation of circle to pass through points
A
(
−
3
,
4
)
,
B
(
3
,
4
)
and
(
−
4
,
3
)
The equation of a circle is
x
2
+
y
2
+
a
x
+
b
y
+
c
=
0
From the coordinates of the three given points we get three equations.
⇒
(
−
3
)
2
+
4
2
−
3
a
+
4
b
+
c
=
0
⇒
3
2
+
4
2
−
3
a
+
4
b
+
c
=
0
⇒
(
−
4
)
2
+
3
2
−
4
a
+
3
b
+
c
=
0
we can simplify the above equation -
⇒
⎡
⎢
⎣
−
3
4
1
3
4
1
−
4
3
1
⎤
⎥
⎦
⎡
⎢
⎣
a
b
c
⎤
⎥
⎦
=
⎡
⎢
⎣
−
25
−
25
−
25
⎤
⎥
⎦
solving the above matrix equation using craner's rule
a
=
0
,
b
=
0
and
c
=
−
25
Putting there values
a
,
b
and
c
in general form we write required equation of circle
x
2
+
y
2
−
25
=
0
On center radius form
(
x
+
0
)
2
+
(
y
+
0
)
2
=
25
Center of circle is
(
0
,
0
)
and radius
=
5.
Hence, the answer is
5.
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Every Point on the Bisector of an Angle Is Equidistant from the Sides of the Angle.
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