Tangent to Circle problem

[Infantry]

I'm having trouble solving

Tangent TB and secant TCA are drawn to circle O. Diameter AB is drawn. If TC = 6 and CA = 10, then CB =?

Any help is appreciated.

 

[Infantry]

Here it is, sketched it quickly.

 

[Deleted member 4993]

I'm having trouble solving

Tangent TB and secant TCA are drawn to circle O. Diameter AB is drawn. If TC = 6 and CA = 10, then CB =?

Any help is appreciated.

Hint:

triangle TBA and triangle BCA are similar. So

AC/AO = TB/AT

And don't forget Pythagorus.

 

[Mrspi]

I'm having trouble solving

Tangent TB and secant TCA are drawn to circle O. Diameter AB is drawn. If TC = 6 and CA = 10, then CB =?

Any help is appreciated.

You should have a theorem which says something to this effect:

If a tangent and a secant are drawn to the same circle from an external point, then the tangent segment is the GEOMETRIC MEAN between the whole secant segment and the portion external to the circle.

Using your diagram, the tangent segment is TB. The "whole secant segment" is TA, and the portion of the secant segment which is "external to the circle" is TC.

So....

TA / TB = TB / TC

If you recall that in a proportion, the product of the means is equal to the product of the extremes, you can write this as

TB*TB = TA*TC

or,

(TB)² = TA * TC