Question

Prove that the tangent at any point (r,β)on r²=a²sin2β makes angle 3β with initial line​

Answer 1

Answer:

Question

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

Solution

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.