Question

In the given figure, AB is a chord, AC
is the diameter of the circle
and CDB = 40°. If AT is a tangent to
the circle at point A, then the
measure of ZBAT is equal to
DK40°
B
T Т.
A​

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]