Question

prove that the tangents drawn to a circle at the end point of a diameter are parallel to each other.

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Answer 1

Answer:

Here AB is a diameter of the circle with centre O, two tangents PQ and RS drawn at points A and B respectively.

Radius will be perpendicular to these tangents.

Thus, OA ⊥ RS and OB ⊥ PQ

∠OAR = ∠OAS = ∠OBP = ∠OBQ = 90º

Therefore,

∠OAR = ∠OBQ (Alternate interior angles)

∠OAS = ∠OBP (Alternate interior angles)

Since alternate interior angles are equal, lines PQ and RS will be parallel.

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Answer 2

Answer:

Step-by-step explanation:

simply make a diameter of the circle and two tangents at the end points of diameter.

we know that tangent is always perpendicular to radius .

so both both tangents will make ∠90° at the end points of diameter.

but these are co-interior angles as the sum of the angles of the same side of diameter is 180°.

therefore the two  tangents will be parallel.

hope you understood.

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