Question:
ΔABC is a triangle inscribed in a circle with centre O. Let α = ∠BAC, where 45° < α < 90°. Let β = ∠BOC. Which one of the following is correct?
ΔABC is a triangle inscribed in a circle with centre O. Let α = ∠BAC, where 45° < α < 90°. Let β = ∠BOC. Which one of the following is correct?
Options:
- cos β = (1 + tan2 α) / (1 – tan2 α)
- cos β = (1 – tan2 α) / (1 + tan2 α)
- sin β = 2 sin2 α
- cos β = (2 tan α) / (1 + tan2 α)
- cos β = (1 + tan2 α) / (1 – tan2 α)
- cos β = (1 – tan2 α) / (1 + tan2 α)
- sin β = 2 sin2 α
- cos β = (2 tan α) / (1 + tan2 α)
Correct Answer: b)
Explanation:
1 We know that, angle subtended by a chord at centre is always double the angle subtended by
‘ it at any other part of the circle.
A
L\
3
B GC 1
LN,
1 SL B= 2a
‘ = cos f= cos 2a ⇒ cos f = 1H ‘
.. _ 1-tan’f
– cos 20 = Lis \
1 We know that, angle subtended by a chord at centre is always double the angle subtended by
‘ it at any other part of the circle.
A
L\
3
B GC 1
LN,
1 SL B= 2a
‘ = cos f= cos 2a ⇒ cos f = 1H ‘
.. _ 1-tan’f
– cos 20 = Lis \