Question

in a circle the angle between tangent and radius drawn at the point of contact is

prove with method​

Answer 1

Answer:

Since, the shortest distance between a line and a point is known as perpendicular which make 90° angle . Thus, The angle between a tangent to a circle and the radius drawn at the point of contact is 90°.

Answer 2

Answer:

Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact.?

Answer

Referring to the figure:

OA=OC (Radii of circle)

Now OB=OC+BC

∴OB>OC (OC being radius and B any point on tangent)

⇒OA<OB

B is an arbitrary point on the tangent.

Thus, OA is shorter than any other line segment joining O to any

point on tangent.

Shortest distance of a point from a given line is the perpendicular distance from that line.

Hence, the tangent at any point of circle is perpendicular to the radius.