Question

Prove that"the lengthof the tangents drawn from an external point to a circle are equal"​

Answer 1

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

$\huge\fbox \red{Proof:}$

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

∠OSK=∠ORK=90

Using Pythagoras Theorem

$ok ^{2} = {os }^{2} + {sk}^{2} ...(1)$

${ok}^{2} = {or}^{2} + {rk}^{2} ....(2)$

Subtracting (2) from (1)

${ok}^{2} - {ok}^{2} = {os}^{2} + {sk}^{2} - {or}^{2} - {rk}^{2}$

$= > {sk}^{2} = {rk}^{2}$

$os = or$

$sk = rk$

Hence proved.