Question

prove that the length of tengent from an external point are equal.​

Answer 1

Answer:

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=90o

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