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In the adjoining figure, AB is the diameter of the circle with centre O. Two tangents $p$ and $q$ are drawn to the circle at points A and B respectively. Prove that $p \parallel q$. Further, a line CD touches the circle at E and $\angle BCD= 110^\circ$. Find the measure of $\angle ADC$.
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$\angle DAB = 90^\circ$, $\angle CBA = 90^\circ$ (Angle between tangent and radius at point of contact is $90^\circ$) (1 Mark)
$\angle DAB + \angle CBA = 180^\circ$ (1 Mark)
Hence, $p \parallel q$ as co-interior angles are supplementary (1 Mark)
$\angle ADC = 180^\circ - 110^\circ = 70^\circ$ (1 Mark)
$\angle DAB + \angle CBA = 180^\circ$ (1 Mark)
Hence, $p \parallel q$ as co-interior angles are supplementary (1 Mark)
$\angle ADC = 180^\circ - 110^\circ = 70^\circ$ (1 Mark)