Question

PT is a tangent to the circle having centre o. if PT =r-1,OT=r,and OP=r+1.find actual lengths of triangle opt

Answer 1

the lengths of tangents will be
TP =3units
OP =4units
in the solution also the cm should be replaced by units.
hope it helps : )

Answer 2

Answer:

The length of sides TP, OT and OP are 3, 4 and 5 units respectively.

Step-by-step explanation:

It is given that triangle OTP is a right angled triangle.

OP = r+1

OT = r

TP = r-1

Using Pythagoras theorem,

$OP^2=OT^2+TP^2$

$(r+1)^2=r^2+(r-1)^2$

$r^2+1+2r=r^2+r^2+1-2r$

$r^2+1+2r=2r^2+1-2r$

$0=2r^2+1-2r-r^2-1-2r$

$0=r^2-4r$

$0=r(r-4)$

$r=0,4$

r is the radius of circle, so it can not be zero. The value of r is 4.

OP = r+1 = 4+1 = 5

OT = r = 4

TP = r-1 = 4-1=3

Therefore the length of sides TP, OT and OP are 3, 4 and 5 units respectively.