Math, asked by tikunu, 3 months ago

73
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 Anonymous
4

Answer:

 \huge \green{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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