Q1 of 49 Page 1

In fig. 1, O is the center of a circle, AB is a chord and AT is the tangent at A. If ∠ AOB= 100°, then calculate ∠ BAT.


As we know that the angle opposite to equal sides are equal.


∴ ∠1=∠2 ……(1)


Sum of all the angles of a triangle is 180°.


∠1 + ∠2 + ∠AOB=180°


∠1 + ∠2 + 100° =180° (given ∠AOB = 100°)


∠1 + ∠2=80°


∠1 + ∠1=80° (From equation 1)


2∠1=80°


∠1=40° …………….(2)


We know that the angle between the tangent and radius is 90° .


∴ ∠1 + ∠BAT=90°


40° + ∠BAT=90° (From equation 2)


∠BAT=50°


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