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Byju's Answer
Standard X
Mathematics
Radius and Tangent to a Circle Are Perpendicular
Question 1 0 ...
Question
Question 10
In figure. If PQR is the tangent to a circle at Q whose centre is O, AB is a chord parallel to PR and
∠
B
Q
R
=
70
∘
, then
∠
AQB is equal to
(A) 20°
(B) 40°
(C) 35°
(D) 45°
Open in App
Solution
Given , AB
∥
PR
∴
∠
A
B
Q
=
∠
B
Q
R
=
70
∘
[
A
l
t
e
r
n
a
t
e
a
n
g
l
e
s
]
A
l
s
o
,
Q
D
i
s
p
e
r
p
e
n
d
i
c
u
l
a
r
t
o
A
B
a
n
d
Q
D
b
i
s
e
c
t
s
A
B
.
I
n
Δ
Q
D
A
a
n
d
Δ
Q
D
B
,
∠
Q
D
A
=
∠
Q
D
B
[
E
a
c
h
90
∘
]
A
D
=
B
D
Q
D
=
Q
D
[
C
o
m
m
o
n
s
i
d
e
s
]
∴
Δ
A
D
Q
≅
Δ
B
D
Q
[
B
y
S
A
S
s
i
m
i
l
a
r
l
y
c
r
i
t
e
r
i
o
n
]
T
h
e
n
∠
Q
A
D
=
∠
Q
B
D
[
C
P
T
C
]
(
i
)
A
l
s
o
∠
A
B
Q
=
∠
B
Q
R
[
A
l
t
e
r
n
a
t
e
i
n
t
e
r
i
o
r
a
n
g
l
e
]
∴
∠
A
B
Q
=
70
∘
[
∠
B
Q
R
=
70
∘
]
H
e
n
c
e
∠
Q
A
B
=
70
∘
N
o
w
i
n
Δ
A
B
Q
,
∠
A
+
∠
B
+
∠
Q
=
180
∘
⇒
∠
Q
=
180
∘
−
(
70
∘
+
70
∘
)
=
40
∘
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Similar questions
Q.
Question 10
In figure. If PQR is the tangent to a circle at Q whose centre is O, AB is a chord parallel to PR and
∠
B
Q
R
=
70
∘
, then
∠
AQB is equal to
(A) 20°
(B) 40°
(C) 35°
(D) 45°
Q.
In the given figure, PQR is a tangent to the circle at Q, whose centre is O and AB is a chord parallel to PR, such that ∠BQR = 70°. Then,
∠
AQB = ?
(a) 20°
(b) 35°
(c) 40°
(d) 45°