Prove that there is one and only one tangent at any point on the circumference of a circle.
Let P be a point on the circumference of a circle with centre O.
If possible, Let PT and PT’ be two tangents at a point P of the circle.
Now, the tangent at any point of a circle is perpendicular to the radius through the point of contact.
∴ OP ⊥PT and similarly, OP⊥PT’
⇒ OPT = 90° and ∠OPT’ = 90°
⇒ OPT = ∠OPT’
This is possible only when PT and PT’ coincide. Hence, there is one and only one tangent at any point on the circumference of a circle.
Concept: Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior, Concentric Circles
Is there an error in this question or solution?