How would this circle proof be set up?

Step-by-step explanation:

Given: Circle O with BT as a tangent at point B.

           T is the midpoint of arc CD.

To prove: (CA)(TB) = (TA)(CT)

Since point T is the midpoint of arc CD,

Therefore, m(arc CT) = m(arc TD)

and m∠CAT ≅ m∠DAT

m(∠ACT) = 90° [Angle subtended by the diameter]

By applying tangent rule in triangles ACT and ABT,

tan(∠CAT) =

Similarly, tan(∠BAT) =

Since tan(∠CAT) = tan(∠BAT)

Therefore,

(CA) × (TB) = (CT) × (TA)

Hence proved.

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