Question

prove that tangents drawn at the end of a diametre of a cirlce are parallel. with the diagram

Answer 1

step-by-step instructions:-

Let AB be the diameter of a circle, with centre O. The tangents PQ and RS are drawn at points A and B, respectively.

SEE THE ATTACHMENT AND THEN THE REST OF STEPS...

We know that a tangent at any point of a circle is perpendicular to the radius through the point of contact.

∴ OA ⊥ PQ and OB ⊥ RS

⇒ ∠OBR = 90°

∠OBS = 90°

∠OAP = 90°

∠OAQ = 90°

We can observe the following:

∠OBR = ∠OAQ and ∠OBS = ∠OAP

Also, these are the pair of alternate interior angles.

Since alternate interior angles are equal, the lines PQ and RS are parallel to each other.

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