Mathematics

Problem

Let

P

be a point outside a circle with centre

O

and radius

r

. A tangent drawn from

P

touches the circle at

T

. (a) Prove that the length of the tangent

PT

satisfies

PT^2 = OP^2 - r^2

. (b) Using your result in part (a), find

PT

when

OP = 10\,\text{cm}

and

r = 6\,\text{cm}

. a. (a) Prove that

PT^2 = OP^2 - r^2

for any point

P

outside the circle. b. (b) Using the relation proved in part (a), calculate

PT

when

OP = 10\,\text{cm}

and

r = 6\,\text{cm}