Q. 404.0( 4 Votes )

In the given figure, O is the center of a circle, AB is a chord and AT is the tangent at A. If AOB = 100° then BAT is equal to


A. 40°

C. 90°

B. 50°

D. 100°

Answer :

In AOB


OA = OB [radii of same circle]


OBA = OAB [Angles opposite to equal sides are equal]


Also, By Triangle sum Property


AOB + OBA + OAB = 180°


100 + OAB + OAB = 180°


2 OAB = 90°


OAB = 40°


As AT is tangent to given circle,


We have,


OA AT


[Tangents drawn at a point on circle is perpendicular to the radius through point of contact]


So, OAT = 90°


OAB + BAT = 90°


40° + BAT = 90°


BAT = 50°

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