Question

# PQ is a tangent to the circle at A, DB is a diameter,$\angle ADB = 30^\circ and\angle CBD = 60^\circ$. Calculate $\angle QAB$.

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Hint: We can easily solve this problem by using the Alternate Segment Theorem i.e. Angle made by chord and tangent at a point on the circumference of a circle is equal to the angle made by that chord in alternate segments. (Alternate Segment Theorem)

$\angle ADB = 30^\circ$ and $\angle CBD = 60^\circ$………………………………(1)
If we refer the figure then we can notice that angle made by chord AB and tangent PQ at a point A on the circumference of circle ($\angle BAQ$) is equal to the angle made by chord AB in its alternate segment ADB ($\angle ADB$).
$\therefore \angle BAQ = \angle ADB$ (Alternate Segment Theorem)
$\therefore \angle BAQ = 30^\circ$ [From (1)]
Therefore, the value of $\angle BAQ$ is $30^\circ$.