#1**+2 **

This one is a little difficult....

Assuming that CD is a tangent, ODC forms a right triangle with OC the hypotenuse and CD a leg

So....the other leg (OD) can be found with the Pythagorean Theorem.....note that OD = OB =the radius of the circle, r

OD = sqrt ( OC^2 - CD^2) and we can write

r = sqrt ( [CB + OB]^2 - CD^2 )

r = sqrt ( [ 14 + r ]^2 - 25^2 ) square both sides

r^2 = [14 + r ]^2 - 625

r^2 = 196 + 28r + r^2 - 625 subtract r^2 from both sides

0 = -429 + 28r add 429 to both sides

429 = 28r divide both sides by 28

15.3 = r

And the diameter is twice this = 30.6

CPhill
Apr 12, 2017