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Byju's Answer
Standard IX
Mathematics
Introduction to Circles
From the foll...
Question
From the following figure, we can say that
A
B
>
C
D
.
If true then enter
1
, else enter
0
.
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Solution
Given,
∠
A
B
C
=
∠
A
B
D
=
70
o
,
∠
A
D
C
=
∠
A
D
B
=
40
o
and
A
B
=
A
C
.
In
△
A
B
C
,
since
A
B
=
A
C
, we get,
∠
A
B
C
=
∠
A
C
B
=
70
o
...... [By Isosceles triangle property].
Also,
∠
A
C
B
+
∠
A
C
D
=
180
o
......[Linear pairs]
⟹
70
o
+
∠
A
C
D
=
180
o
⟹
∠
A
C
D
=
180
o
−
70
o
=
110
o
⟹
∠
A
C
D
=
110
o
.
Then, in
△
A
C
D
,
∠
A
D
C
+
∠
A
C
D
+
∠
C
A
D
=
180
o
......[By angle sum property]
⟹
40
o
+
110
o
+
∠
C
A
D
=
180
o
⟹
150
o
+
∠
C
A
D
=
180
o
⟹
∠
C
A
D
=
180
o
−
150
o
=
30
o
⟹
∠
C
A
D
=
30
o
.
Since,
in
△
A
C
D
,
∠
A
D
C
>
∠
C
A
D
⟹
A
C
>
C
D
.
⟹
A
B
>
C
D
......[Since, given
A
B
=
A
C
].
Therefore, the statement is true and
1
is the answer.
Suggest Corrections
0
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Q.
In the above fIgure.
∠
B
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C
=
60
0
and
∠
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If true enter 1 or else enter 0.
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