Question

5.7 Prove that the length of the tangent drawn from
external point to a circle 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=90

o

Using Pythagoras Theorem,

OK

2

=OS

2

+SK

2

............(i)

OK

2

=OR

2

+RK

2

............(ii)

Subtracting (ii) from (i),

OK

2

−OK

2

=OS

2

+SK

2

−OR

2

−RK

2

⟹SK

2

=RK

2

∵OS=OR

SK=RK

Hence, proved

hope it's correct and help full