Circle center O has tangents PQ and PR. PQ is 24cm and radius is 7cm. Calculate the length OP
Show workings
We can begin by drawing a diagram:
P-------O-------R
|
|
|
Q
We can see that OP is the radius of the circle. We are given that the radius is 7cm. Therefore:
OP = 7cm
Alternatively, we can use the Pythagorean theorem to find the length of OP. We know that PQ is 24cm and PR is also 24cm (since they are tangents from the same point). Therefore, QR is 24 + 24 = 48cm. We also know that OR is the radius of the circle, which is 7cm.
Using the Pythagorean theorem, we have:
OP^2 + PR^2 = OR^2
Substituting the given values, we get:
OP^2 + 24^2 = 7^2
Simplifying and solving for OP, we get:
OP^2 = 49
OP = 7cm
Therefore, OP is 7cm, which we already found earlier.