Question

prove that the lengths at any point of a circle is perpendicular to the radius through the point of contact​

Answer 1

Correct question :

• prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact

To prove :

• OP ⊥ AB

Contraction :

• join OQ intersecting at R

Solution :

OQ = OR + RQ

but OP = OR ( radius )

OQ = OR + RQ

OQ > OP

OR < OQ

we know that among are the line segment joining the point O to a point on AB the shortest one is perpendicular

∴ OP ⊥ AB Hence Proved

Answer 2

CorrecT QuesTioN :

• Prove that the tangent at any piont of a circle is perpendicular to their radius throught the point of Contact.

To ProvE :-

• OP perpendicular to AB

ConsTructioN :-

• Draw OQ which is intersecting at R

SoluTioN :-

The Question is to prove the given statement

• OQ = OR + RQ

But, OP = OR ( Radius )

• OQ = OR + RQ

• OQ > OP

• OR < OQ.

We Know that among are the line segment joining to the point O from a point AB, The shortest is a perpendicular.

$\boxed{ \bold{ \red{</u><u>★</u><u>He</u><u>nce \: </u><u>OP</u><u> \: perpendicular \: to \: </u><u>AB</u><u>}{} }{} }{}$