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6. AB is the diameter oneof circle and AC is its chord.
The tangent at C intersect the produced diameter AB
at D. Given that AB = 10 cm, AC = 8 cm Z BAC = 30°
then BD will be equal to :
(a) 6 cm
(b) 8 cm
(c) 10 cm
(d) 4 cm
74
Answers
Answered by
4
Answer:
∠ACB=90 ∘ [∠ from diameter]
In ΔACB
∠A+∠ACB+∠CBA=180 ∘
∠CBA=180 ∘ −(90+30)
∠CBA=60 ∘
_________ (1)
In △OCB
OC=OB
so, ∠OCB=∠OBC [opp sides are equal]
∴∠OCB=60 ∘
Now,
∠OCD=90 ∘
∠OCB+∠BCD=90 ∘
∠BCD=30 ∘
_______ (2)
∠CBO=∠BCO+∠CDB [external ∠ bisectors]
60=30+∠CDB
∠CDB=30 ∘
________ (3)
from (2) & (3)
BC=BD [ opp. ∠.S are equal]
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