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Byju's Answer
Standard XII
Mathematics
Trigonometric Ratios of Compound Angles
In an isoscel...
Question
In an isosceles triangle with
A
B
=
A
C
, the bisectors of
∠
B
and
∠
C
meet at
O
. Produce
B
O
upto
M
then prove that
∠
M
O
C
=
∠
A
B
C
.
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Solution
In
Δ
A
B
C
with
A
B
=
A
C
∠
B
=
∠
C
(given)
In
Δ
B
O
C
∠
M
O
C
=
∠
O
B
C
+
∠
O
C
B
=
1
2
(
2
∠
O
B
C
+
2
∠
O
C
B
)
=
1
2
(
∠
B
+
∠
C
)
∵
∠
B
=
∠
C
∠
M
O
C
=
1
2
[
∠
B
+
∠
B
]
=
1
2
∗
2
∠
B
=
∠
A
B
C
Hence Proved.
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Similar questions
Q.
Bisectors of angles
B
and
C
of an isosceles triangle intersect each other at
O
and
A
B
=
A
C
.
B
O
is produced to a point
M
on side
A
C
. Prove that
∠
M
O
C
=
∠
A
B
C
.
Q.
The bisectors of
∠
B and
∠
C of an isosceles triangle with AB = AC intersect each other at a point O. BO is produced to meet AC at a point M. Prove that
∠
MOC =
∠
ABC.