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Joint Entrance Examination
Mathematics
Circle
Question 81
Question 81 of 219
Medium
MCQ
Let
y
=
x
+
2
y=x+2
y
=
x
+
2
,
4
y
=
3
x
+
6
4y=3x+6
4
y
=
3
x
+
6
, and
3
y
=
4
x
+
1
3y=4x+1
3
y
=
4
x
+
1
be three tangent lines to the circle
(
x
−
h
)
2
+
(
y
−
k
)
2
=
r
2
(x-h)^2+(y-k)^2=r^2
(
x
−
h
)
2
+
(
y
−
k
)
2
=
r
2
. Then
h
+
k
h+k
h
+
k
is equal to:
A
5
B
5
(
1
+
2
)
5(1+\sqrt{2})
5
(
1
+
2
)
C
6
D
5
2
5\sqrt{2}
5
2
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Official solution
\[(h,k) = \left( {{{5.5 + 5( - 2) + 14\sqrt 2 } \over {10 + 7\sqrt 2 }},{{35 + 21\sqrt 2 } \over {10 + 7\sqrt 2 }}} )\right.\] \[h + k = {{50 + 35\sqrt 2 } \over {10 + 7\sqrt 2 }} = 5\]
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