What is the relation between the tangents at the extremities of a diameter of a circle?
The tangents at the extremities of diameter are parallel to each other
Proof:
Consider a circle with centre O and diameter AB having tangents as PA and RB as shown
∠OAP = 90° …radius is perpendicular to the tangent at the point of contact
∠RBO = 90° … radius is perpendicular to the tangent at the point of contact
⇒ ∠OAP = ∠RBO
∠OAP and ∠RBO are alternate angles between lines PA and RB having transversal as AB
As alternate angles are equal lines, PA and RB are parallel
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