Question

prove that the tangents drawn at the ends of a diameter of a circle are parallel

Answer 1

$\textbf{Answer is in Attachment !}$

Answer 2

$\huge\boxed{\fcolorbox{red}{pink}{❥ANSWER}}$

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.

Ncert solutions class 10 chapter 10-6

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. (Hence Proved).