Question

Prove that the tangents drawn at the ends of a diameter of a circle are parallel.​

Answer 1

Answer:

In geometry, the tangent line to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve

Step-by-step explanation:

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tq

Answer 2

Solution

➝ 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.

➢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).