Question

10th class-Mathematics-tangents and secants to a circle-

To prove that the tangent at any point of a circle is perpendicular to the radius of the circle at the point of contact.

Answer 1

Hope this will help you.. tq u..

Answer 2

Given : A circle C (0, r) and a tangent l at point A.
To prove : OA ⊥ l
Construction : Take a point B, other than A, on the tangent l. Join OB. Suppose OB meets the circle in C.
Proof: We know that, among all line segment joining the point O to a point on l, the perpendicular is shortest to l.
OA = OC  (Radius of the same circle)
Now, OB = OC + BC.∴ OB > OC⇒ OB > OA⇒ OA < OB
B is an arbitrary point on the tangent l.
Thus, OA is shorter than any other line segment joining O to any point on l.
       Here, OA ⊥ l