Question

prove that the tanget at any point of a circle is perpendicular to the radius through the point of contact.?Answer it fast!!!!!!!!

Answer 1

Step-by-step explanation:

answr

search

What would you like to ask?

10th

Maths

Circles

Tangent to a Circle

Prove that the tangent at a...

MATHS

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

MEDIUM

Share

Study later

VIDEO EXPLANATION

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.

Answer 2

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.

Step-by-step explanation:

mark me as brainlist