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Joint Entrance Examination
Mathematics
Straight Lines and Pair of Straight Lines
Question 293
Question 293 of 303
Medium
MCQ
In a \[\triangle A B C\], suppose
y
=
x
y=x
y
=
x
is the equation of the bisector of the angle
B
B
B
and the equation of the side
A
C
A C
A
C
is
2
x
−
y
=
2
2 x-y=2
2
x
−
y
=
2
. If
2
A
B
=
B
C
2 A B=B C
2
A
B
=
B
C
and the points
A
A
A
and
B
B
B
are respectively
(
4
,
6
)
(4,6)
(
4
,
6
)
and \[(\alpha, \beta)\], then \[\alpha+2 \beta\] is equal to
A
42
B
39
C
48
D
45
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Official solution
\[
A
D
:
D
C
=
1
:
2
4
−
α
6
−
α
=
10
8
α
=
β
α
=
14
and
β
=
14
\begin{aligned} & A D: D C=1: 2 \\ & \frac{4-\alpha}{6-\alpha}=\frac{10}{8} \\ & \alpha=\beta \\ & \alpha=14 \text { and } \beta=14 \end{aligned}
A
D
:
D
C
=
1
:
2
6
−
α
4
−
α
=
8
10
α
=
β
α
=
14
and
β
=
14
\]
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