Question

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

Answer 1

if helpful. mark it as brainlist

Answer 2

$\huge{\red{\underline{\mathfrak{Explanation:}}}}$

_____________________________

We have to prove that the tangents drawn at the ends of a diameter of a circle are parallel.

So, we will draw a circle and connect two points A and B such that AB becomes the diameter of the circle.

Now, we will 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 (As they are also alternate interior angles)

So, it can be said that line PQ and the line RS will be parallel to each other.

$\huge{\blue{\mathfrak{Hence,Proved}}}$