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19/06/2021 11:39 am
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Prove that the tangents drawn at the ends of a diameter of a circle are parallel.
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19/06/2021 11:42 am
First, draw a circle and connect two points A and B such that AB becomes the diameter of the circle. Now, draw two tangents PQ and RS at points A and B respectively.
Now, both radii i.e. AO and OP are perpendicular to the tangents.
So, OB is perpendicular to RS and OA perpendicular to PQ
So, ∠OAP = ∠OAQ = ∠OBR = ∠OBS = 90°
From the above figure, angles OBR and OAQ are alternate interior angles.
Also, ∠OBR = ∠OAQ and ∠OBS = ∠OAP (Since they are also alternate interior angles)
So, it can be said that line PQ and the line RS will be parallel to each other.