# 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 toA. 40°C. 90°B. 50°D. 100°

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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