Prove that the perpendicular at the point of contact to the tangent to a circle passes through the center.
The word "tangent" comes from the Latin word 'tangere,' which means "to touch."
Answer: The perpendicular at the point of contact to the tangent to a circle passes through the center is proved.
A tangent line or tangent in geometry means a line or plane that intersects a curve or a curved surface at exactly one point.
Let O is the center of the given circle.
Draw a tangent LP touching the circle at point P.
Draw RP ⊥ LP at point P, such that point R lies on the circle.
∠OPL = 90° (radius ⊥ tangent)
Also, ∠RPL = 90° (Given)
∴ ∠OPL = ∠RPL
Now, this can only be possible when center O lies on the line RP.