In the given figure, AOB is a diameter of a circle with centre O. If angle BOD = 120°, find angle ACD.
(A) 30°
(B) 40°
(C) 60°
(D) 90°
Answers
Answer:
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Step-by-step explanation:
Given- O is the centre of a circle of which AOB is a diameter.
CD is another chord, intersecting AOB
∠BOD=120 °
To find out- ∠ACD=?
Solution-
∠AOD=180 ° − ∠BOD
= 180 ° − 120 °
=60 ° ....(linear pair).
Now ∠AOD is the angle subtended by the minor arcAD to the centre and ∠ACD is the angle subtended by the minor arc AD to the circumference at C.
∴∠ACD = 1/2 ∠ACD
= 1/2×60 °
=30 °
Answer:
30
Step-by-step explanation:
Given-
O is the centre of a circle of which AOB is a diameter.
CD is another chord, intersecting
AOB
ˉ
.
∠BOD=120
o
To find out- ∠ACD=?
Solution-
∠AOD=180
o
−∠BOD=180
o
−120
o
=60
o
....(linear pair).
Now ∠AOD is the angle subtended by the minor arcAD to the centre and ∠ACD is the angle subtended by the minor arc AD to the circumference at C.
∴∠ACD=
2
1
∠ACD=
2
1
×60
o
=30
o