Question

ab is the diameter of a circle and ca is its chord such that angle bac = 30. if the tangent at c intersects ab extended at d. prove that CB =bd

Answer 1

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]

Step-by-step explanation:

Answer 2

Step-by-step explanation:

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