Question

prove that in the lengths of tangents draw
from an extent points to a circle use equal​

Answer 1

It is known that a tangent at any point of a circle is perpendicular to the radius through the point of contact. Therefore triangle OPA is congruent to triangle OPB by RHS criterion. Thus, it is proved that the lengths of the two tangents drawn from an external point to a circle are equal.

Answer 2

Step-by-step explanation:

The attached figure shows two tangents, SK and SR drawn to circle with center O from an external point K.

To prove that: SK=RK

Proof:

Normal and tangent at a point on the circle are perpendicular to each other.

∠OSK=∠ORK=90°

Using Pythagoras Theorem,

OK²=OS²+SK²............(i)

OK² =OR² +RK²............(ii)

Subtracting (ii) from (i),

OK²−OK² =OS²+SK² −OR²−RK²

⟹SK²=RK²

∵OS=OR

SK=RK

Hence, proved