A circle has radius 3 cm. A tangent is drawn to the circle from point P, which is 9cm from the circle's centre. How long is the tangent?

Question

A circle has radius 3 cm. A tangent is drawn to the circle from point P, which is 9cm from the circle's centre. How long is the tangent?

Answer 1

Let r = the circle's radius = 3

 

Therefore, we know that the distance from the center of the circle to the point where the tangent intersects the circle is 3.

 

The problem says that P is 9cm from the center, so we have two sides of the triangle, so we can solve for the length of the tangent.

 

Let a = the height of the triangle = 3cm

Let b = the length of the triangle = the length of the tangent

Let c = the hypotenuse of the triangle = the distance from P to the circle center = 9cm

 

a² + 3² = 9²

a² = 81 - 9 = 72

a = √(72) = 8.4852cm