there are two concentric circles. QP is a chord for the larger circle, while being tangent to the smaller one. if the larger radius is 14 and the smaller radius is 6, find the length of QP.

25.298 or 8√ (10)

Step-by-step explanation:

In this problem half of chord QP and the radius of the smaller circle form a right triangle whose hypotenuse is the radius of the larger circle. We can use the pythagorean theorem to find the missing leg, which is half the lentgth of the chord to find the total lenght of teh chord.

a=radius of larger circle

b=half of chord

c=radius of smaller circle

a²=b²+c²

a²-c²=b²

14²-6²=b²

196-36=b²

160=b²

b=√160

b=12.649

2b=chord length

2 (12.649) = 25.298

The length of the chord is 25.298 or 8√ (10)