Question

PT is tangent to a circle with Centre O. OT = 56cm
TP = 90cm
find OP =?​

Answer 1

Step-by-step explanation:

the answer for OP is 106 cm.

Answer 2

The length of OP is 106 cm.

Given:

OT = 56cm and TP = 90cm

To find:

The length of OP

Solution:

The tangent TP, the circle's radius OT and the line segment OP form a triangle that is right-angled at T.

Since TP is the tangent, OT is perpendicular to TP.

So, angle OTP=90°

We will use the Pythagoras theorem to obtain OP's length.

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

Using the values,

$OP^{2}$=$56^{2} +90^{2}$

$OP^{2}$=3136+8100

$OP^{2}$=11,236

OP=√11,236

OP=106 cm

Therefore, the length of OP is 106 cm.