Question

Prove that the lengths of tangents drawn from an external point to a circle are equal.

OR

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

Answer 1

Question is proved .Hope it helps you

Answer 2

$\bf{ \green{given}}$

tangent AB and AC are on points B and C.

$\bf{to \: prove}$

AB=AC

$\bf{ \blue{construction}}$

join O to A

O to C

and..

O to B

$\bf{ \purple{proof}}$

$\sf{in \triangle \: aoc \: and \: \triangle \: aob}$

$\sf{ \angle \: oca = \angle \: oba( \: both \: 90 \degree)}$

$\sf{ob = oc \: \: (radius \: of \: circle)}$

$\sf{oa = oa \: (common)}$

$\sf{ hence\: \triangle \: aoc \: \cong\: \triangle \: aob(by \: rhs)}$

hence

$\bf{ab = ac \: \: (cpct)}$

$\huge{lhs \: = \: rhs}$

$\bf{ \underline{proved}}$

$\huge{ \gray{thanks}}$