Prove that a tangent is perpendicular to the radius through the point of contact - Maths - Constructions

Question

Prove that a tangent is perpendicular to the radius
through the point of contact

Koka Sri Lakshmi Divya Sai · Accepted Answer

$Let a circle with center C(0,r) and a tangent at point A is l Take a piint B,other than A on the tangent l Join OB.Suppose OB meets the circle in C OA=OC(radius of the same circle) \Rightarrow OB > OC \Rightarrow OB > OA \Rightarrow OA < OB B is an arbitary point on the tangent l OA is shorter than any other line segment joining O to any point on l Her e OA ⊥ l$

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Prove that a tangent is perpendicular to the radius through the point of contact.