If tangent at C  , intersects extended diameter  A B , of a circle at  D, if BD=BC   then ∠BAC  is equal to ____°.

# If tangent at  , intersects extended diameter  A B , of a circle at  D, if   then  is equal to ____°.

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### Solution:

If tangent at  , intersects extended diameter  A B , of a circle at  D, if   then  is equal to 30°.
Given: DC is the tangent. AB is the diameter. OB and OC are radius of circle.
….(Length of tangent drawn from external point is equal)
Tangent is perpendicular to radius at point of contact.    Angle subtended by semicircle is right angle.

In  ,    (angles of equal opposite sides)(1)
In   ,
( angles of equal opposite sides) (2)
By exterior angle theorem,
….(From 2)

Put   in place of  ,

Put   in place of   ,

Put  ,
In  ,
By angle sum property,

Hence the measure of   is equal to  .

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